I book a bike on GWR trains quite regularly. It's a bit late for you now, but the best way to do it is when you buy your ticket on the GWR website. There is an email address over which it is possible to book bike reservations with your tickets: GWRreservations@gwr.com.
Whilst I always book a bike, I don't necessarily travel on the train for which I always have a reservation and I've never had a problem. Though I don't travel to or from London, and they might be a bit more fussy there.
On Class 800 trains, bike spaces are distributed throughout the train. Each bike space theoretically holds two bikes, but it is difficult to fit more than one in. The bike space also doubles as luggage space, so sometimes you will have to shift suitcases out as well. On five carriage trains the bike spaces are in the B and D carriages, towards the centre of the train. Ten carriage trains are two five carriage trains hooked together, so four bike spaces. On nine carriage trains there are five bike spaces, in carriages B, D, J (two here) and one in first class. Be warned, station announcements don't advertise all of these spaces, though there is usually a bike symbol on the carriage at the appropriate doors.