It would depend on first, where would Bruce be located at time of attacks? If he was in another room and heard screaming, shots fired, etc. maybe he could have had a plan. Note the apocryphal story of his instant thinking with Vic Damone's two bodyguards. Although it may not have happened, Stirling Silliphant did venture that it was in keeping with BL's though processes. So imagine if he was in another room and then he kicks the door with a huge slam, which would freeze whoever was in the room, and maybe hit one of the bad guys (or of course maybe one of the good guys); in that frozen moment, he could have taken out frozen guy with gun. I say 'could' as a possibility; again it would depend where the gun was pointed. Now there have been police studies where often at close range a person will miss. The odds in favor of the good guy go up as the adrenaline shoots up in the shooter; with a drug-crazed guy holding the weapon he's not going to have precision, and anything he hits will be an accident. So it's possible BL could feint and with some luck the barrel could be in a 'safe zone' and he would then close in.
Second scenario is that BL is in another room and does the stealth thing. But he has to act fast, of course, because people are being shot. Or were they first tied up at gunpoint? (It's a good idea to decide beforehand whether you'll allow yourself to be tied up. Maybe they'll be nice to you? Or should you just fight now and risk being shot, etc.? Again, statistics show that a person can be shot but still overcome attackers. It seems that at least the first shot is statistically survivable. So one has to decide all this beforehand.)
Or if Bruce was in the same room when the crazies burst in, he would zero in on the guy with the gun. Again, as above, he would have had a chance that the guy would miss before BL was able to close. I remember a famous case where a Russian pilot stole a MIG and flew it to the West. In the hanger of the MIG was a guard with a rifle, and although he was shooting at the pilot, the pilot was zigzagging and he wasn't shot. And there are also studies where it's estimated a police officer (example) with a gun facing a guy running at him from 20 feet may not even be able to draw his firearm. So of course there's a lot of variables if BL was 'there.' Maybe he would have thrown something at the guy's face to distract him (this is taught to some school kids if a gun man ever appears in class -- throw everything you have at him; in other words they are taught to fight back).
So in summation Bruce could have been shot and still be able to move and take the gunman out, or he could have been shot and disabled. Or he could have avoided being shot and game over for the bad guys. With the screaming and so on I don't see him running to get the police. If there were time, he would have considered this, I think. But his life experiences would have given him a cool head in this case, and decide the best course of action.
Anyway, thanks for the thought problem! Never considered that one, before. I also think about what 'I' would do in such a situation. Better to analyze before it ever happens.