Updated July 22, 2023
This is a pretty straightforward $1-$2 per bag, though in these inflationary post-pandemic tough-service tip-crazy times, many people fork over a five, ten, or even twenty no matter how many bags are involved. For a couple of bags, $5 seems fair; any more than that, $10's a good toke.
As always, it depends on the service. If it's especially fast and friendly, it might be more. Or if a bellman hustles up to your car, unloads the bags from the trunk, waits while you check in, and accompanies you to your room, giving you a running commentary all the while on everything from the hotel and neighborhood to the best hangouts and hookers (if you're a male by yourself), you might go a little extra.
Typically, you tip a bellman at the room, unless you're not going to your room immediately and you want your bags to be waiting for you when you get there; then you tip when a bellman first handles your bags.
We've never heard of bellmen pooling their tips, so your guy will keep what you hand over.
On Carrying Your Own Bags to Your Room