No real experience with Rim Tours, but I've talked to them a few times - we're thinking about doing the White Rim too. They really took their time answering, even though we were basically asking if we could do it on our own. We hiked down to the White Rim and watched a few folks on a 4x4, and a few bikes. It was amazing - we were out on Murphy's Hogback, and the rise up to that didn't look like something I would want to drive or ride, but everyone does it, so I guess it's do-able!
Let us know about it when you go!