If you're staying in Sedona, I imagine you're thinking South Rim. Which is too bad, North Rim is much nicer. The previous link was for UTAH tourism so North Rim would be much more accessible to them. It's a 4-hour drive to get from South to North. Or a two-day hike, take your pick
South Rim is crowded. Cars everywhere. Buses and busloads of tourists everywhere. No riding on the rim trail. I guess one could bring their bike and hop around in the park, but there are many, many cars and buses on narrow roads and I don't really know if that'd be much fun. Your best bet might be to park the car at the outdoor center and ride the bus to the sights.
It's a decent road ride from Williams up to the Canyon, about 50 mi. The buses get irritating but no big deal, road is wide enough. I've been intrigued by the ride from the Canyon to Desert View and Cameron (east on hwy 64) but I haven't ridden it yet, maybe I'll do it this year.
If you're a dirt rider, there are published maps about the old stage route from Grand Canyon to Flagstaff. I believe it's outside the park, and I believe there are some pretty good vistas but don't know if that's what you're looking for.
My recommendation is: Drive to North Rim. Take an extra day. MTB all over the place and have a ball! There's a hikers/bikers campground right out on a promitory ridge, it very seldom sells out and you can practically be guaranteed a nice campsite - as usual, if you can't drive there it's not crowded.
Have ridden the south rim about 10 times, the north rim only once. Road riding only (NO offroading).
Pedaling from Sedona will be a workout: Oak Creek Canyon is 'UPhill' toward Flagstaff and would be best ridden early in the day; less traffic then, but road is winding switchbacks/UP/narrow. It would necessitate an overnight stay before you arrive at the south rim.
Pedalin' the south rim is best done before the motorhome crowd starts off after their morning coffee. Ride from Park HQ to Desert View, very scenic but hilly and altitude 7,000+ feet.
North rim, park at Jacob Lake and pedal to the rim; altitude about 1,000 feet higher than south rim. Hardly any traffic, NO services 'til you arrive at GC Village. Suggest you stay overnite (make reservations) and pedal back the next day. NO bikeshops for about 300 miles so pack what you need in spares.
Also bring lotsa water (and drink!) and use sunscreen even if it is cloudy. You'll burn easy at that altitude.