id say it depends on what youre doing in the gym, and probably how far/what type of riding youre doing to/from the gym.
people have made comments about how to take your stuff with you…you dont need 10 more people to make suggestions on that, so i wont bother.
as far as riding home after a workout, ive often thought the same thing, and ive yet to take my bike to the gym.
honestly, i dont think im as alert after pounding some weights hard for an hour. i certainly dont feel the same sitting in my car, driving. a lot of times i feel tired and pretty beat up after a workout, and i wouldnt want to ride feeling like that.
if i were you, my decision would be based on how far/where id be riding. for me, my gym is only 6-7mins from my house. thats if i hope on the highway. and theres a couple on/off ramps and such that i just wouldnt want to mess with on a bike if my body wasnt feeling fresh.
on the other hand, if i lived in a small town where my gym was simply 5-10 minutes away riding on roads with relatively low speed limits, i might be more inclined to ride to and from sometimes.
now i will simply hypothesize about something: if you had say, a workout consisting of heavy loads- 85%+ of your 1rm’s, and were thus placing a high demand/high damage to your CNS, i see a very real possibility that you could have delayed muscle reaction after a tough workout. again, something to take into consideration, based on what kind of riding youd be doing.