That’s exactly right: You call a casino, ask to be connected to VIP Services, get a host on the phone, and tell him/her who you are and how large of a bankroll you’re planning on bringing with you on your upcoming trip to Las Vegas. (Be sure to use the word "bankroll," which specifically enumerates the amount of money you’re bringing to gamble with, as opposed to the total amount you’re bringing for gambling plus strippers, hookers, limo rides, nightclubbing, and the like.)
Then you can ask him what kind of speed he and his joint’ll show you in return for your play ("speed" being a sort of code word for comps).
If you haven’t done this before, may we respectfully suggest that you don’t call your favorite casino first? It’s a good idea to get your "sea legs," so to speak, by practicing on hosts at joints you don’t care about, before tackling a host at your favorite gambling hall. After calling a few different casinos and talking to hosts there, you’ll be an old hand at negotiating deals with casino marketing representatives.
We can also suggest reading our books Comp City and Whale Hunt in the Desert. Comp City, though a bit dated in the comp-criteria department, has excellent information on scouting casinos. Whale Hunt describes the whole process in detail, only from the host’s point of view; it’s always good to know what your business associate is thinking while you’re negotiating a deal with him. You’ll also find excellent information on the care and feeding of casino hosts in More Frugal Gambling.
By the way, even if you’re bringing "only" $3,000 with you for a four-night stay, you should call and talk to a host anyway. You might not get much speed at Bellagio or the Wynn (though it doesn't hurt to start at the top; you never know what promotions they’ve got going on or how desperate they are for players), but you’ll add to your negotiating experience and get some comparative parameters.
Also, lots of hosts know one another. A host at a higher-level joint might give you a referral to one at a casino that’s more in your budget; then you can ask for that host personally and invoke the other host by name, so you’re not coming completely out of left field.