What you've got is an Advanced Purchase ticket, which is only valid on the train(s) shown on the ticket. From the National Rail page on Advanced Tickets:
You may not start, break and resume, or end your journey at any intermediate station except to change to/from connecting trains as shown on the ticket(s) or other valid travel itinerary.
So, on your way from London to Birmingham, your ticket doesn't entitle you to end your journey short at Bicester. In practice, as there aren't barriers at Bicester station, you could probably get away with it, but be aware that if there was a spot ticket check at the station that day you'd risk being made to buy an anytime ticket from London to Bicester (or face prosecution as a fare evader). Unlikely, but possible.
Coming back, your ticket is only valid to start in Birmingham and end in London. It isn't valid to start part way. (An Off-Peak or Anytime would be). Again, you could probably get on the train in Bicester, as there's no barriers, but your problem is when they do a ticket inspection on the train. They'll most likely do one shortly after Birmingham, and quite possibly another close to London. When they check your ticket it won't already be stamped, so they'll then know that you weren't on the train at Birmingham when they did the first check. You're therefor in line for buying a new ticket, and possibly a penalty fare too (but IIRC Bicester isn't a penalty fare station so you might be OK on that)
It's possible that you could get away with it, perhaps with no ticket check after Bicester, or the first check not until after Bicester, or a ticket inspector not noticing, or taking pity on you, but it's a risk as you're not supposed to be doing that on that ticket. Chiltern are a friendly rail company, with good customer service, but it's still a risk...