From Mondays to Saturdays, the X4 runs hourly to Milton Keynes, with departures (from Stop B4 at the Food Centre) starting at 0835 (not Saturdays) and going through to 1735. There's then a final bus at 1845. Buses leave the Rail Station (Stop 37) 6 minutes later. The journey time is 50 minutes.
On Sundays, the service runs every 2 hours, from 1015 to 2015.
Other buses (e.g. services 89 and 1B) operate between MK and Northampton, but take much longer.
There are frequent trains, with many journey times being less than 20 minutes.
http://www.travelinesoutheast.org.uk
Chris