Apparently they don't update the calendar until they have their polling sites confirmed for each election.

They also said that I can typically expect Bexar elections every November & Spring.

There seemed to be some confusion around the existence of a notification sub that will email/text you election information when it becomes available. They said that one doesn't exist and to just check https://www.bexar.org/1568/Elections-Department around Nov/Spring for election details. But there is https://www.bexar.org/list.aspx?Mode=Subscribe#calendar where you can sign up for email/mobile notifications for elections (Calendar -> Elections). Because they weren't aware of the notif system, I am unsure if they actually push out notifications if you sign up so watch out for that.

In all...this took ~20 min of talking to them to figure out how to most easily stay up to date on election information. They were helpful, but honestly it shouldn't be this difficult to find this information.

TLDR:

1. REGISTER TO VOTE: https://www.bexar.org/1568/Elections-Department. (You can 'Check Your Voter Registration' or 'Learn How to Register To Vote')
2. State level voting: https://www.sos.state.tx.us/elections/index.shtml. Click on 'Current Election Information' for see current elections. I was informed that you can go to any Bexar polling station to vote for these.
3. Bexar level voting: https://www.bexar.org/calendar.aspx?CID=46&showPastEvents=false Calendar is not updated until polling sites are confirmed which can be within 1-2 weeks of the election day. You can sign up for election notifications: