Of course there's room for new answers and there might be new discoveries. But there's also an FAQ entry and some other answers you can find by searching "Bering" in the sub. FAQ: https://www.reddit.com/r/AskHistorians/comments/1fmljj/how_come_america_was_not_discovered_via_the/cabrg0t/ by u/Reedstilt

Another thread I think had a good answer:

https://www.reddit.com/r/AskHistorians/comments/4qtdpv/was_there_any_movement_back_and_forth_across_the/d4w6q9r/ by u/The_Alaskan