Wet roads are definitely more slippery. This morning that was a lot of water on the roads but none in the air, and when I put my foot down at one stop it kept sliding out from under me. The big thing is to slow down so you are reducing the force needed to keep the tires from slipping. Good rain gear is also important, because if you’re wet, you’re wet in very high winds on a bike.
I ride to work every chance I get, and I work in an office. My boss rides, so he isn’t a real bear about showing up with riding boots, but I have my own standard for how I should be dressed at work. If a corporate customer shows up, I don’t want to be seen sitting around in leather pants.
I have small soft bags on my bike. Shoes, rain gear and when the weather is variable spare gloves ride on one side, my lunch on the other. For a sport bike, you might look at a tail bag. It’s like a tank bag, but rides behind you.