Train yourself not to grip the bars tightly. A light grip is not instinctive so you have to concentrate and practice it at first.
You really can control the bike with only a light grip most of the time. For example, if the bar wants to turn to the left, let the grip put pressure on your left palm and between the thumb and forefinger. Holding your left arm steady will stop the bars from turning without you having to put a death grip on the bars. A side benefit of a light grip is it can help you ride relaxed.
If all else fails, over time you will build callouses, and the blisters should stop being a problem.