I can't find anything which suggests against light exercise before the test.
I am still experiencing nausea in pregnancy which is likely to be worse after not eating. Cycling normally suppresses the nausea. The alternative is to get the bus, and I get travel sick at the best of times, and the bus will take longer.
The cycling will be at a leisurely pace, no more strenuous than walking for the same amount of time. Pre-pregnancy I regularly cycled to work before I'd had breakfast.