Yeah but not because of fear of being judged or anything but because I have less incentive. If getting a random dude to have sex with me would be an ego affirmation of how gorgeous and witty and amazing I was, I'd probably (if single) have tons of fun chasing guys for sex. But pretty much most women could get a guy to have sex with them just by the virtue of wanting sex, so it won't do shit for my ego as it would to a guy. In fact, I'd just give some dude an ego boost in return for an orgasm which I can easily give myself any time. I really think that if men got no ego boost for having sex with women they'd also be much less interested in the chase.

I'm not bi, I'm totally straight, but I've been I'm a few different situations in my life where I flirted with women (even online when I was younger and pretended to be a guy, irrelevant story), and it was exciting not because of the woman herself but because I had to put in a special charm. My whole approach was so different then how I acted with men - it was like this very fun game to play where sign of attention gave me a sense of great accomplishment.

Just to add something - man who acts disinterested doesn't attract me but putts me off. Also gender roles. Since I expect women to be hard to excite, if I was a man I wouldn't take initial restraint from her end as an insult to my attractiveness. But being a girl, I would take a man who isn't interested in me as him not finding me attractive and "working for it" would be the opposite of an ego boost, so.id be sexually repulsed toward such man. I do get some ego boost when men show very strong interest but that means that for a man to attract me he'd have to initiate.

Tl; Dr - feeling extremely attractive and wanted (ego boost) is what creates a lot of sexual attraction. Men get an ego boost from getting a girl to have sex with them as it is an affirmation of their attractiveness. Woman could get sex with a random guy just by asking (not always of course but in theory) so it is no ego affirmation at all to initiate and be accepted. Very high male interest and attraction as demonstrated through initiation and more does start to provide that needed ego boost- problem is that his interest is enough for the ego boost so sex itself won't always follow.