So if this were to exist the prologue would be the infinity war (I decided to write this idea now before this gets jossed). With a bunch of all powerful objects presumably blasting things there would be a lot of weird energy flung around. And since there is both a time and a space stone this energy could go literally anywhere. Of course most of space and time isn't all that interesting. No-one cares if a powerful energy source appeared in empty space just after the dawn of time only to disappear again centuries before life develops anywhere. Or if a lost civilization appears for a split second to fast for anything to register. But eventually something's going to hit something.
So the prologue would end with a rock, more of as chunk of old brick really, hit with enough energy to exist in to times at once. Something that's only noticed by 2 kids, one in 1930 something and one in 1990 something (or there abouts) when each of them happed to be in the same back ally in Brooklyn.
So this story would be about modern Bucky meeting past Steve. From Bucky's point of view it would one of the child-finds-a-secret-world stories, never mind that the secret world is the past (after all the past is another country right?) and for Steve it would be a person-visits-from-an-other-word story, because the future is weird. I figure Steve can visits the future for a bit but gets sick real fast. Bucky can stay in the past for ages but starts to fade too after awhile. They never figure out if it's just because Steve is physically weaker the Bucky or if it's just easier to go back then forward. They have all these theories but they're only guessing.
Obviously they would have lots of adventures. I figure Bucky would swipe medication for Steve from the future once he understands how sick he was (never mind the fact that your not supposed to just give people medicine without doctor approval) including an inhaler he either traded from a classmate or sole from. The also hatch a scheme to get Steve vaccinated by slipping him in with his classmates to take the place of a kid whose patent didn't want them to get the jab but never gave the paperwork to the teacher for the exemption. Or maybe just robed a needle.
I'd say Sarah finds out eventually but it's saving her kids life so she goes with it.
So the two grow up as friends. Bucky doesn't have to explain much to people in his time because he usually goes to Steve's but people know he has a friend how can't go out much on some other street. To Steve's neighbours Bucky's around enough that they just assume his family just lives around somewhere.
Then angst happens.
Maybe Bucky's parents die so he tried to stay in the past but that doesn't work.
Sarah does die, so the only people who know about their situation is the 2 of them.
Bucky feels bad because he's from the future, he should have looked things up or something. Buts they've had talks about it before (because Bucky's defiantly a sci-fi nerd. And come on, time travel) and Steve says it's not fair on Bucky to know that kind of the thing, and Steve defiantly doesn't want to know. So Bucky promises to never tell Steve what will happen and avoids anything about history if possibly.
WWII happens and Bucky is inspired by Steve's continuous F4's to join the army in his time, plus he doesn't know what else to do with his life. He spend his leave with Steve and they work out to send messages or letter with the stone or something.
Steve becomes Captain America. Bucky only meets Steve once like this when he's doing the stage show thing and is shocked and terrified. He might have been avoiding history but everyone knows Captain America, it's one of these pop culture things. And while he may not have paid attention to the details Cap is pretty famous for how he dies. Steve is upset about not getting to fight and Bucky's silently panicking so lets slip that he rescues the 107th (something he only remembered the name of because it was the unit Steve's Dad was in). Bucky clams up after that and Steve doesn't push because the both made a promise not to try and mess with the timeline (so much sic-fi has warnings about the dangers of this so they desperately try not to). Steve also pretty happy now to know he will make a difference so he misses how off Bucky is.
Bucky goes back to his time and simultaneously tries to remember everything he's ever heard about Cap and desperately not go look it all up. He figures the less he knows the less likely he'll ether break time or make a self fulfilling prophecy.
He and his unit go to deal with an uncover weapons cash that turns out to have ancient weapons form WWII. Hydra weapons. Hydra weapons power by the tesseract, also known as the Space stone.
I don't know if I want them to be attacked or have the tesseract energy react to the little time stone Bucky has but something happens. Maybe a Hydra agent inside Shield shows up and tries to wipe out the team as a cover up. Whatever it is, Bucky gets sent back to Steve time but not to Steve.
He ends up in the battle where Hydra capture the 107th. (like calling to like with the Hydra weapons.) Since he landed in mud and it's night no-one really notices him and he dumps his out of place modern gear as soon as he realises what's happening. The 107th surrender to Hydra, he's got nowhere to run and is obviously American so gets lumped in with them. There are a lot of prisoners from different groups at the camp so no one questions it much. Bucky is hopeful because he knows Cap come here but he's also scared because he doesn't know if he'll die before that & if Hydra finds out about him he'll be worse then dead. The stone also isn't working so he's stuck here.
Steve find out about the 107th and trusts Bucky to never steer him wrong so goes to rescue them. He can't fully explain why he needs to but Peggy has his back so he heads off like in the movie. Since he comes back with his best friend people figure out that's why he went.
Steve, of course, is shocked to find Bucky strapped to the table and worried that he can't go back to his own time. The Howlies figure something's up but with so many prisoners lost paperwork is put down for not finding his records and none of them say a word otherwise.
They properly find out the truth, also Peggy. Maybe Howard too, I don't know.
Bucky falls as usual but I'm not sure if he gets caught by Hydra again or not.
Maybe when he's falling the stone finally works again or crumbles into dust as it's power finally gives out putting people back in their proper places.
So Bucky gets back to were he was. If it wasn't Hydra that attacked he get cleaned up by the Military and gets an honourable discharge. He no longer has the stone so he can't go back to Steve but maybe he tracks down the Howlies that are still alive and isn't so alone.
But if Hydra was the one to attack that might try again to cover it up so he goes and disappears tying to find out just how deep the corruption goes. Maybe he becomes the Winter Solider that way.
Either way when Steve wakes up in the future he adapts faster that people thought. He's not going to let them know Bucky showed him tech and stuff before.
After the battle of New York, when the whole world knows he's alive, he's just setting at a cafe, sketching, when Bucky sits next to him.
Maybe they just confuse everyone with being such good friends even though no-one can figure out why. Or maybe they go out to secretly clean up Shield.
Either way they're back together and on even footing and I can't think of what else would happen so, The end.