Can a woman bring in her handbag

I was there last Saturday and there was a "clear bag policy".

Yes but some events check them

https://www.alamodome.com/plan-your-visit/clear-bag-policy

Alamodome has a clear bag policy. It is better to check for the specific event

Yes

At the Alamo City Comic Con there was no requirement for transparent bags. Check for each event.

Only of it's transparent. And it's subject to search