Welcome to FT!

Stansted immigration times can be extremely difficult to predict - what we can say for certain is that you will have to queue for a desk because ID cards cannot be processed at the e-gates, so that will certainly add some time.

30 minutes is not uncommon. Link that with a bus to the terminal, walk to Border Control and a few minutes the other side getting to the bus station and it might be tighter than you think - plus there’s obviously the risk of a late arrival. As you identify you can buy, for £7 (currently) a passport Fast Track if you want more certainty - this allows a maximum of 50 passengers per hour, so should be comparatively quick and almost certainly would give you a better chance of catching your bus.