Sounds a bit to me like you are trying to have your cake, eating it, then getting frustrated at the conditions in which you are able to have and eat that cake.
No offence meant (seriously), but if you are struggling to afford or are starting to feel the pinch at having all 3 then despite what you want, you should cut back at least 1 of them. The bike, sounds to me the least required. Yes there is a reason for all 3 to be worth having, but justifiable to your living costs as well?
I have a diesel van for work, and a bike. I could quite easily buy a car and justify that into my equation but simply, I can not afford the luxury of a car as well, so unfortunately, I go without one :(
lose the bike. the loss of that could help offset the tax your having to pay. tax, unfortunately is a pita but no way of getting around, and trust me, (from twice previous experience), its not worth declaring sorn and nippin out in it hoping to not get caught...
If you don't want to sell either of the 3, then perhaps you should look at trying to get a better paid job to suit your lifestyle, or get a second job :P