A qualified yes.
Large males can weigh-in as much as 360 Kg (790 lb), that's over three and a half times the weight of an adult male human (like the one typing this answer, who frankly needs to lose some excess pounds). Running whilst carrying the extra weight is going to be noticeable, but shouldn't present much of an issue for sprinting or a paced distance run. It'd approximate a healthy, muscular adult male human carrying an average 11 year old piggyback (with the mount still being able to swing arms), not comfortable, but doable.
As to speed; male grizzlies have been recorded reliably at Yellowstone at 48 km/h (30 mph) with short bursts of about 18% higher than that. Somewhat slower with a living back-pack.
Note; males inland weigh less than on the coastal regions.
Small females weigh as little as 100 Kg (Yucon river area, inland), so nearer the weight of a muscular adult male human. Perhaps an adolescent or small woman might be OK here.
The issue of staying-on whilst at a gallop is something I'll leave to the writer, but worth bearing in mind that although the rhythm is much like a horse's gallop - there is no saddle, bridle or stirrups unless you can convince it to wear them. Good luck to any of your characters that try to do that.