Actually, that's a good question.
Not really since he never does that
in the movies.
Here's a list of scenes in the cave involving Bruce/Batman:
Batman 89
-Bruce leaves his party to check the security tapes before going to Axis Chemicals.
-Batman brings Vicky Vale back to the batcave for protection and the film of her camera. Obviously he's dressed as Batman since he's got company.
-Bruce reads the file about his parents. Still Dressed as Bruce when Vicky walks in the cave he suits up since
he's going out.
Batman Returns
-Bruce slides in the batcave to go suit up. he's on his way out for action.
-After the 1st fight with Catwoman, Bruce is in the process of
removing his costume in the batcave.
-Bruce plays D.J. to mess with Penguin's speech. Dressed as bruce.
-Bruce is fixing the batmobile when alfred comes in with an invitation. Again, Bruce is dressed as Bruce.
Batman Forever
-Batman is lecturing Dick about revenge in the batcave while undressing out of frame. comes out as Bruce.
-Bruce is getting patched up by Alfred. Naked Bruce Wayne from the waist up.
-Bruce shuts down the batcave. dressed as bruce since he's quitting being Batman.
-Bruce suits up
before going out to fight Two-Face and Riddler in a final showdown.
Do I really have to try remembering
Batman & Robin?
Fine! There's 2 scenes where Batman is suiting up in the cave
before going out to fight.
Batman Begins
-Bruce discovers the cave
-Bruce crawls in the cave after coming back in Gotham. He stands in a tornado of bats.
-Bruce sets up the cave with lights and checks out the waterfall.
-Bruce makes his weapons.
-Batman brings Rachel back to the cave. He takes off his mask as soon as she's passed out.
-Bruce suits up for the final showdown.
So... When does Bruce Wayne stay Batman while in the cave,
in the movies ? 
