I can't think how it would make any difference. You do need to flush out the contrast dye quickly afterwards by drinking and peeing lots, and the cycling may leave you less hydrated, so you'll need to drink even more to be peeing lots. I would try to do this before cycling home.
I didn't do it deliberately or even know at the time, but cycling to my consultations was probably big plus. The clinicians have to assess how fit you are to decide which treatments are appropriate and what your life expectancy is from other factors. Turning up with cycling rucksack and cycling helmet is probably one of the best ways to show that. However, unless you've been told otherwise, you are unlikely to have a consultation that day, as they have to wait for the MRI results from a radiologist and the next MDT meeting.