You can take a bus from Towcester to Bicester via Central Railway Station and Buckingham, Tesco (Services) in around 1 h 59 min.
How to get from Towcester to Bicester
From Towcester, Brave Old Oak PH bus to Central Railway Station, bus to Buckingham, Tesco (Services), then bus to Bicester Town Centre, Manorsfield Road (Bus Stand 3). 1 h 59 min £14. From Towcester, Saracens Head Hotel bus to Woodford Halse, Demand Responsive Area (Woodford Halse), bus to Banbury, then train to Bicester North. 2 h 1 min £85. From Towcester taxi to Bicester. 25 min £71. From Towcester drive to Bicester. 25 min £4.