Most of the time the vertical clearance is unlimited passing through a Bascule Bridge.
I don't think I've ever passed through one that once opened still had a limited vertical clearance for my mast. There are a few bascule bridges that I've transited where there could be an issue of horizonal clearance if your beam was large enough to force you to pass under the raised portion of the bridge in order to maintain horizontal clearance from a train trestle or a bridge abutment. If that's the case here your best bet is to call the operator or the bridge authority. But you might just have to do your own math.
With the bridge you mentioned it looks like it's a two leaf opening that you pass through in the center of a channel.
See photos here: Treasure Island
It looks like you should have no worries.
Maybe some one familiar with that bridge will weigh in.