No.
Unless, you knew your exact latitude, longitude and the date.
If you were on the equator, and cycled to and from work on a road running exactly East - West, then, on (or about) the 21st March and the 21st September, your shadow (assuming travelling westwards to work) would be exactly in front of you, and, on your return journey (Eastwards) it would be exactly behind you.
However, you could wake up with a hangover and not get to work until 11.30 (local time) and go home an hour later at 12.30 (local time) and the same would apply - your shadow would be in-front / behind you just as if you had done a full day.
Your bike is not tall enough to throw an accurately measurable shadow - the errors associated with measuring the shadow's angle are to great to calculate an accurate time - even if you knew the time of year (date), latitude and longitude.