An alternative is to cross the Ouse at Stony Stratford, turn left at the lights in Old Stratford and pick up the cycle way just before the road comes out on the A422, and this takes you to the Deanshanger roundabout (option to rejoin the Passenham Road or use the cycle bridge)
@JamesT
Not sure what the river's like at Passenham for your return journey, but the road is quite low lying there so could be flooded: https://check-for-flooding.service.gov.uk/river-and-sea-levels?q=Buckingham%2C%20MK18%201AA&v=map&lyr=ri,ti,gr,rf,ts,tw,ta,mv&ext=-0.925059,52.021027,-0.812388,52.067878
An alternative is to cross the Ouse at Stony Stratford, turn left at the lights in Old Stratford and pick up the cycle way just before the road comes out on the A422, and this takes you to the Deanshanger roundabout (option to rejoin the Passenham Road or use the cycle bridge)