London Road is a key access route for east-side residents and businesses alike.
I cannot see how east-destined commercial traffic benefits from being routed along the bypass then down the existing narrow roads such as Church Street and Market Square.
I was a Bicester resident Jan 1991 until Dec 1993 - prior to Sheep Street commerce was ruined from pedestrianisation (I was on the local Chamber Of Commerce objecting to that act of vandalism); and a few years before redevelopment of the old Tesco site (now a Sainsburys and cinema).
Commercial traffic is unlikely to use Church Street and Market Square. It'll access the centre via St John's Street or Launton Road.
It is however, much more of an issue for residents that find themselves the wrong side of the tracks and facing a journey two or three times as long as it currently is. Although, in reality they have that already given how often the crossing seems to fail and block the road for extended periods of time. I would also expect that the increase in rail traffic from the current test/training runs means the barriers are down for so long that the route is virtually unusable.
This has been a bone of contention for years as there seems no realistic solution for replacing the crossing with an alternative for road traffic and no available diversionary route - Gavray Drive is the obvious one but they'd have to knock down Aldi. However the rail authorities haven't done themselves many favours by appearing to tell the locals they'll just have to lump it.
(As an aside, as a current resident of Bicester I am very glad that your objections to pedestrianisation were ignored so we can now enjoy a civilised traffic free town centre!)
(And shouldn't this discussion all be in the thread related to future consultation not current construction?!)