Steve believed him for now, even though it brought more questions about who exactly woke him up and for what reason. It was truly frustrating that he was from an earlier time period than Bucky, he had no idea what was going on and therefore he couldn't help out as much as he could. He'd still do his best, but Steve couldn't ignore that little fact.

"...Let's head back to my apartment." From there, he could at least offer Bucky food or water or maybe patch him up a little more even if his injuries were healing. Provide him support and someone that Bucky could count on even though he was in the dark about many things.