They can't. They can't stop people of a particular race from coming to a particular place on particular dates.
They can enforce nuisance-abatement laws - public drunkenness, nudity, noise, no-turn-signal, and so on. Occupancy guidelines for lodging could be enforced. Businesses should be allowed to close at will.
Apart from that, one runs afoul of free speech and free association rights. I think a motel should be allowed to say, "I won't rent to a black person during this time period," but that's not within the current understanding of civil rights.
Well, you're right, and in principle I agree. However, didn't some of the businesses get sued for closing ("discrimination)? IIRC some were even "forced" to put up signs in the windows welcoming the bikers! Or maybe I'm confusing this with another event.