A word for female bonding

Womance is the word you are looking for.

There is allegedly homance but I have never heard it in use.

"A womance is a close but non-sexual relationship between two (or more) women, a form of homosocial intimacy. The word is the female equivalent of a bromance, being a portmanteau of the words woman and romance."

Someone had already suggested girlcrush: feelings of admiration and adoration which a straight girl has for another girl, without wanting to bang said girl. a nonsexual attraction, usually based on veneration at some level.

UrbanDictionary defines girlcrush as:
A (normally) straight girl's crush on another girl, often a celebrity. Is mostly platonic in nature. A girl who is girlcrushing must by definition be straight, otherwise it's just a regular crush.