Warwickshire were at 277 for 6 against Somerset, with Yates scoring 69 runs, Burgess unbeaten on 63, and Bethell also contributing with 60 runs to the team's total.
Warwickshire fought back superbly in the final session to reach 277 for 6 against Somerset on a hard-fought opening day of their Vitality County Championship match at Edgbaston
Needing a win to maintain their pursuit of Division One leaders Surrey, Somerset chose to bowl and their seamers reduced the home side to 165 for 6, but Jacob Bethell, with 60 not out off 134 balls, and Michael Burgess (63 not out from 79) added an unbroken 112 in 30 overs.
The seventh-wicket pair bailed out a top order which contributed little apart from Rob Yates's 69. Craig Overton and Josh Davey both took two wickets but Somerset's bowlers mixed good balls with too many loose offerings which prevented them building the required pressure.
Warwickshire, mired in a relegation battle, were very grateful for the work of Bethell and Burgess as they try to build a position from which to push for their belated first Championship victory of the season.
After Overton, captain in the absence of Lewis Gregory, won the toss, Somerset's new-ball bowling was inconsistent. Warwickshire openers Alex Davies and Yates added 52 in 13 overs before the former departed furious at himself after edging a footwork-free waft at Kasey Aldridge to wicketkeeper James Rew.
On a pitch offering some but by no means lavish assistance to the seamers, Warwickshire advanced comfortably enough to 94 for 1 before a change of ball reversed the flow. Will Rhodes, having moved to 22 in assured fashion, was bowled off-stump by one from Overton that held its own and three more wickets followed for 19 runs in 44 balls.
Hamza Shaikh, making his first first-class appearance for Warwickshire, collected his first boundary with a luscious on-drive off Jake Ball but fell in the fast-bowler's next over when he sliced a drive to Tom Lammonby to backward point. Yates, having struck 13 boundaries, played on to Davey who then produced a peach of an outswinger to find Ed Barnard's outside edge.
Bethell and Dan Mousley, fresh from the free hitting of The Hundred, knuckled down to add 21 in 65 balls before Mousley was drawn into a drive at Overton and former Warwickshire batter Andy Umeed held a stinging catch at second slip.
At 165 for 6, the home side was in jeopardy, but Bethell and Burgess batted beautifully. Bethell smashed a 15-ball T20 half-century against Northamptonshire earlier this year and his explosive batting qualities are well-known, but he now showed technique, concentration and selectivity to dig his team out of trouble.
The 20-year-old reached his fifth first-class half-century from 107 balls and laid the perfect platform for Burgess to attack at the other end.
Burgess lifted Jack Leach for six over long on and then cleared the ropes twice more in an over off the spinner to pass 50 from 66 balls to add to the century he struck against Somerset at Taunton seven weeks ago. It was a stirring fightback from the Bears which left a compelling day evenly-balanced at its conclusion.