Can I bring a bottle of wine inside?

For a Hollywood Bowl event , yes. For a leased event , no.

Last night you could bring a bottle of wine but not glass.

You can bring wine into a Hollywood Bowl event only, not leased events.

Depends on the event

Is Grease a non-leased event?

Yes

See Ron Niv's answer. ^ It is important to know if it is a good bottle of wine. They have trash cans at the gates that get many bottles (if it is a non-sponsored event).

Yes, you can.