accessibility – Bitcoin Wallet Question

I have a nice sum of bitcoins in a particular account. The account is with a “bank” that does cryptocurrency conversion. This place is charging me $$$ for codes (IMF, COT, Tax, etc.).
I need a bitcoin wallet to access my cash without paying these ridiculous fees. Is the bitcoin wallet universal? I mean, can I obtain a bitcoin wallet from a third party; like through this site? Or, can I only get the bitcoin wallet from the “bank” where I have the account? I ask, because I need to access the bitcoins through bitcoin atm… Thanks.