What I would do (note: this is illegal, but I don't think it is immoral (see last paragraph) or that it is likely to be detected):
If the gates are open at Bushey, go through and board the train shown in the itinerary.
If the gates are closed at Bushey but there is a member of staff stood beside them, show them the ticket and ask to be let through.
If they refuse, or there is no member of staff nearby, touch in with an Oyster card and touch out at Euston. Resume use of the advance ticket at that stage.
For next time: a ticket from Bushey to Lancaster is the same price as a ticket from Watford Junction to Lancaster via London. However, there are some cheaper tickets from Watford Junction to Lancaster that do not involve going via London, so do check for the availability of these before booking from Bushey. Such a ticket would only be valid on Virgin Trains and using it from Bushey, as well as being illegal and more likely to be objected to, would involve going via London without paying the premium for doing so. Due to the broken way fares are set on the British railway, there are no cheaper tickets from Bushey to Lancaster avoiding London.