Good luck on that, Toby.
About the only place you may find a cattle drive, especially one that would take other folks along, would be at a dude ranch.
There was one up here a few years back where they moved about 500 head to a ranch about 200 miles away. It took a lot of coordination to get permisson from all involved, the state, other ranchs, law enforcement, etc.
I had the dubious pleasure of participating in a short drive back in '62, but that was only 200 head and we drove them about 40 miles, which still took 2 1/2 days. Since there were only 3 of us, it was a lot more work than it was fun.
But, don't give up,, find one and enjoy yourself,,, you only live once.
Google: Cattle Drive Vacation
There is one every spring in the Nicola Valley ending up in Kamloops, BC. Short drives with wagons and a camp every night. Hugh McLennan has a syndicated radio show, "Spirit of the West" (and a small cattle operation in the area) and will have information on this drive. His web site is http://www.hugh-mclennan.com/
The only 'cattle drive' I ever rode was abt 10 miles long. It was in the spring of 1962. The truckers wanted more to truck the cattle to the sale barn than the cattle we were driving--scrubs, mostly--would bring at auction, so we drove 'em alongside the highway, over a bridge--they really didn't like that bridge--& right up the main street of the town to the sale barn. Then we rode up to where a wet precinct crossed a county road for about a quarter of a mile, tied our horses, & had some beer.