If you did the bike booking during the purchase you'll be fine - the bike reservation tickets will come out of the machine alongside your travel tickets. I only got in trouble because I did my bike booking over the phone.
I bought the ticket from thetrainline.com then phoned GWR to make the bike reservation separately. I foresee problems...
I didn't realise until too late that GWR let you book bike spaces online at the same time as booking your ticket*, or I would have bought the ticket directly from them.
*other operators don't, so I assumed...
Don't worry, the GWR bike reservation system is broken.
I don't use Paddington, but no-one ever checks bike reservations elsewhere for this very reason. You may get some jobsworth there, but I think it's unlikely.
It's difficult to find the bike spaces on the new trains, so for your information:
On five carriage trains, one compartment in the second and one in the fourth carriage.
Ten carriage trains are two five-carriage units coupled together, so as above.
Nine carriage trains have compartments in the B, F, J (two compartments) and K carriages.
Each compartment is supposed to hold two bikes, but it's difficult to get the second one in (pretty much impossible if you use the recommended hook). Compartments are at the end of the carriage nearer the centre of the train. They double at luggage space, so sometimes you have to throw a few suitcases out.
Some trains have bike symbols by the doors to show where these compartments are. However GWR are as confused by the layouts of these trains as everyone else, so they aren't always in the right place.
There are a few of the old trans still running. If you are lucky you will get one of these.