How important is it to hold handles on exercise bike?

I find it really uncomfy and prefer to not hold on the handles and sit up straight and cycle is it ok to do this or will I not burn as much etc?

It's not the most ideal position for sitting on a bike as it stresses the back to sit straight up and doesn't really create the best supported pedal stroke. You won't be able to put out as much power in other words sitting straight up. And, by sitting bolt upright you are not engaging your core. Shame, oh shame!

However, on an exercise bike you are not having to worry about absorbing bumps, so you're fine in that regard even though you could get a lot more out of your session by bending forward with a properly arched back. Correct cycling posture must facilitate the pedaling action. Another issue is the tractor wide saddles with all that cushion they put on exercise bikes. Terrible stuff which makes it hard to get comfy. Much better with a normal race saddle, minimal cushioning and a proper pair of cycling shorts with a chamois - but that's a different discussion. You can still bend forward into proper cycling position even though they provide a John Deer riding mower tractor seat on the exercise bikes.

It all brings up the question of what you are trying to get out of your session in terms of training.

Break the training zones down into something easy like....

1. Old lady pace
2. Chatty pace
3. Feel good hard
4. Feel bad hard
5. I am going to die
6. Flat out

You'd probably be fine sitting bolt upright for "old lady pace", but would struggle on anything above that.

My suggestion, if you prefer a bolt upright position, is to seek out a recumbent exercise bike as you can engage what needs to be engaged a lot better on a recumbent bike than sitting bolt upright on a bike if you don't want to bend forward.. My other suggestion if you stay on the upright bike is to bend over and engage those glutes and your core!!! It's exercise after all and you're there to burn and work the big muscles. :-)

Laying down the power climbing a ski hill (Zone 4 or feel bad hard)...




And really grunt climbing here (Zone 5 or I'm going to die)...




On the other hand, if you just like tooling along in "old lady pace" and getting minimal calorie burn while you enjoy listening to your music, have at it by sitting upright and fiddling around with the bike....