Yes, you are.
AFAIK all the trains from Exeter to Plymouth are now IETs/Azumas (they're called IETs on GWR). There used to be truncated HSTs just doing the Exeter to Cornwall run but are being phased out (these are the ones which have the capacious bike compartment at the end of coach A). You can check online if your train is one of these as they won't have a First Class carriage. The trains that ply between Cardiff and Plymouth have also switched to IETs. Check where your train originates from but if Paddington it will be a regular IET. In the unlikely event you have booked a Cross-Country, this will be a Voyager and you have booked a bike space.
At the station, the electronic boarding signs will tell you where the bike spaces are - there may be one or two depending on whether the train is 5, 9 or 10 coaches long. You just find the correct zone (which is marked on the platform) to know where to wait. AFAIK, GWR have now sorted out their bike booking numbering and your booking might refer to a specific slot. But I really wouldn't worry about this unless there is an issue and it will in any case give you further support. There may well be luggage where your bike is supposed to go!
What I would say though is that getting your bike on the train is usually really OK. There are some holiday trains that can be over-full (you have a booking!) but mostly the bike spaces are empty. I travel with a folder but rarely fold it - I just put it unfolded into the bike space (no reservation) unless a cyclist needs it. Exeter can be busy and I would certainly recommend a reservation, which you have. The worst of it is a bit of pushing and shoving to get your bike onto the train, into the space and onto the hook. I don't take my luggage off until the bike is on the train. The whole thing is an appalling design but you should be fine.
It is very quick to get from Plymouth station to the ferry terminal but I am presuming you have left yourself plenty of time to allow for any train problem.
