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BoA has a secured card that graduates. Cap 1 -pulls all three credit bureaus; SDFCU does not graduate but does not require a HP.
Wells Fargo also has a secured card, but it's really hit-or-miss if it graduates into something unsecured down the road. If the BoA denial is recent, I would call and ask if they would consider you for their secured card with the HP you already took.
BOA go for it. Best secured card out there just make sure you do the pc to 123 rewards after they approve you for the regular card. U can call or do it thru a chat I believe. Also look at your local credit union mine has no anual fee which is great and can graduate just like boa.