One option is dear Madam (and do not use the surname), but it is rather impersonal. It gets around the problem though.
As a woman, ocassionally you get a letter which has the wrong title on it - it's not massively offensive, just a bit irritating - it's usually just ads anyway.
"Ms" is a modern invention, to solve problems like this, partly. Some people don't like this expression.
But if I was in your situation, I'd use Ms here. It isn't very important, everyone knows its just a greeting. If you do not know her, and you don't have access to some database (creepy) it's totally understandable that you have to make an educated guess, or use Ms.
I'd focus on the rest of the content instead.
And don't forget that the correct way to end a letter that starts with "Dear Ms" is either "Yours sincerely" or "Sincerely yours". Nothing else! Many non native speakers don't know this and write something else, creative, instead, sounding rather silly. Americans sometimes write "God bless" or something similar. It's sweet and I personally don't mind it, but it's not the correct form and most Brits can't stand it. Indians write all sorts of elaborate stuff to end formal letters, making them sound.... silly.