First of all don't ask,, just bring it in.
If you get confronted and they suggest putting your bike in the luggage room (most hotels have them) go for it if you have a beater bike. If you have a slammin TT/tri or carbon bike, you look the guy in the eye, and (embellish if necessary) ask, "can you guarantee that my $5,000$ bike will not get damaged in that room?" That person will choke.. they don't want that responsibility.
Then if they still insist and it comes down to having to leave. You get stern, and demand that they book you a hotel room of comparable quality and price in a nearby location and assist you in getting there. Hotels are about service, and if they wont' budge on policy then the least they can do for inconveniencing you is to give you some service. And always go to the top.
There's a good chance by this point they'll just get lazy and let you take it into the room.