Bonner reached 34 and Holder 43 to trail a frustrated England by 109 runs with six wickets remaining as a late shower brought play to an end.
England's Mark Wood, speaking to BT Sport, said: "Today was indifferent. We started poorly then dragged it back,they dug in well at the end. Our attitude in field was good we fielded with good purpose and intensity. The way we came back and showed good character was important.
"We need a couple of wickets to get into this line up, we know Jason Holder is a fantastic cricketer. They nullified that crucial reverse swing period well when we were keen to take a couple wickets.
"We were not as consistent as we needed to be at first. Our lengths were poor, we didn't quite get it right. I tried a little bit too hard, I put too much pressure on myself.
"When myself and Ben Stokes were bowling in partnership we were clear in our plans and stuck to our guns well, we just couldn't get the breakthrough."
Opener John Campbell was the first to go when he was caught down the leg side for 35 from a Craig Overton delivery.
Overton then took a smart catch as captain Kraigg Braithwaite chased a quick and wide ball from Wood on 55 with the hosts on 101-2.
Ben Stokes then got his reward as he forced Shamarh Brooks to drive at a wide ball and edge to Joe Root at first slip on 18 with West Indies on 111-3.
Jermaine Blackwood then edged onto his thigh pad for the ball to ballon up to Overton at gully as Chris Woakes claimed his wicket with the Windies on 127-4.
Momentum appeared to be with the tourists before Bonner and Holder dug their heels in to blunt the Three Lions' attack in the final session to ensure the hosts hold the edge in the first Test.
When asked what England need to do on day three, Wood said: "We'll find a way to take wickets on this wicket, early wickets will be key. The new ball should be helpful to get the ball moving somehow."