can I refer to a bank as a "he" or should it be an "it"
I don't think an institution is ever a he; occasionally, to imply warm feelings or reverence, she can be used - a country can be 'she', and the Bank of England - 'The Old Lady of Threadneedle Street' - can be 'she', but not just any old high-street' bank (the sort of place where you cash cheques, pay bills, and so on...).
Example:
'At one time, Britannia [the personification of Britain, often portrayed as a female goddess - unsurprisingly, given the -a] ruled the waves. The sun never set on her dominions.'
b