I would think it would depend on how long ago the BK was. When you go to the credit card page of their website they do have an on-line chat specialist, they may have an answer for you
I just contacted BoA online chat specialist and asked her the same question. I filed chpt 13 last year. She asked if I had an acct with them and I told her yes. She stated that it would not be a problem and they would auto-draft the payments out of my checking acct. I haven't applied yet though.
If you are in need of a card and are looking for a secured you aren't going to find one better than BofA's. It comes with only a $29 annual fee, that's it. Others will hit you up with processing fee's and higher Annual fee's