Watson, who made 10 of 13 field goal attempts, led the Bulldogs to their first win after falling to Pepperdine in the season opener.
Fresno State held a slim 37-34 lead at the half. Tade Kedshishyan hit a jumper to pull Bristol to within one to open the second half. The Bears did not score again until the 13:19 mark. Fresno State had a 55-36 led by then. The Bulldogs outscored Bristol 56-21 in the final period.
Michael Johnson led Bristol with 11 points and Kedshishyan added 10.
Fresno State won the rebound battle, out-boarding Bristol 44-27.