Steve is a pretty religious guy, all in all, so if he starts spending more time in church that is usual (Bucky dutifully observes the Sunday mass and celebrates major holidays with enthusiasm, but not much more) no one really minds. Until it's obvious he's desperately trying to atone for something that's eating him up inside.

Now, I'd be delighted if the Avengers thought he was discovering (his) homosexuality and is conflicted about it (because I never get tired of people assuming Steve is repressed when he's actually comfortable with his bisexuality), but this step can be skipped. What I want is for someone to confront him eventually and discover that Steve feels the crushing guilt of being thankful for what happened to Bucky. And it kills him, because he wouldn't wish Bucky's fate on Red Skull, and here he is waking up every morning with a smile on his face because his beloved Bucky was unwillingly subjected to a fate worse than death which landed him on Steve's doorstep in the future. Because Steve figures he would have landed the plane in the ice had Bucky lived, anyway, and this way Bucky is there with him, instead of rolling in a reasonably fresh grave (Steve's first thought upon waking in the 21st century was that Bucky must be rolling in his grave).

Bonus: Bucky is confronted with Steve's guilt.