Just so you're aware, assuming that's an advance ticket you're talking about, what you suggest is not technically legitimate as you're joining short, so there's a chance you could end up getting stung for a higher fare.
However (not encouraging anyone to break the rules) as the journey booked involves a cross-London transfer, the chances of being caught are probably almost nil as you could have easily made the transfer on foot.
Perhaps you could look at advance tickets from Bristol direct to Stansted airport. These start at ^13.00 and go up to ^27.00. Not only would you be sticking to the ticket's conditions, but you could also be saving even more money. The
FGW▸ website actually quotes for this journey, even when the journey continues into the next day:
22:35 Bristol Temple Meads 00:33 London Paddington Train FIRST GREAT WESTERN 01h 58
00:33 London Paddington 04:10 London Liverpool Street Transfer n/a 03h 37
04:10 London Liverpool Street 05:00 Stansted Airport Train NATIONAL EXPRESS EAST ANGLIA 00h 50
I tried for 22nd July and it came up at ^13.00
Edit: I've just noticed you've posted about this fare whilst I was typing this reply