Okay, read through the whole FAQ - the bank acquisition is accurate, but there's a notable bug where the event won't always trigger when stuff is unlocked.
So, earliest you can get the bank is 1905 - Five years after obtaining 20,000 population. If the bank doesn't show up in Jan 1905, spend down to less than $2000 on hand and keep clicking on the advise button, it'll eventually trigger the bank.
A side note, this also may be required for other missing items like Library, Extra Land, etc... though I've still not seen a library.
Huh, that's interesting. Good to know!
I talked here and there to the person who dumped the game and preserved Sim City (also why I linked it in the header on the left side.) There was some information iirc about how programming wasn't finished/bugged: