you really don't need to shower and change your clothes. You can if you want to ride your bike fast and push your physical limits, but generally casual biking won't make you sweat more than if you were walking.
What do you mean by casual biking? Walking home takes me a half hour or longer. Biking is less than 10 minutes according to my bike computer. Big time difference. Plus if it's hot I spend a lot less time in the sun on the bike, making biking less sweaty than walking. And I can carry a lot more cargo more comfortably.
