I tend to share Hound Dog's point of view: I will not apply or re-apply antiperspirant or deodorant before I ride, first because I don't think any will quite do the job, and second because I too believe that a good sweat is healthy and cleans the toxins out of your body. (Quite unscientific point - I should check this out in the literature sometime.)

But if one MUST use something, I'd strongly suggest using a deodorant rather than antiperspirant, for all the reasons cited above by others.

After a ride, if I must be in a car for more than a few minutes, I'll usually change into cleaner clothes made of non-cotton fibers (wrap around skirt - which allows for modest removal of shorts - and some tshirt which allows modest removal of sportsbra if needed). That takes care of the short-term smell. But a shower ASAP is in order, of course...

I'm quite sure only non-riders will notice the smell. Too bad for them.