Have you ever tried it? Unless you've got some unusual bacterial/skin issues, you can probably ride to work in clean clothes, after bathing, work all day, ride home, and not smell.
Especially if you use deodorant. It's really stale, old, sweat, that smells. And it takes a while for it to set in. More than the normal 8-10 hours we work.
When I biked to work, I'd wear a normal T-shirt and some shorts, then swap on slacks and a dress shirt. Hell I used to go work out at lunch, and I'd just wear my under-shirt to the gym and toss the regular dress shirt over it again. First few times I specifically asked people if I smelled, because paranoia.