My normal warm-up routine includes a bike ride. After I got a flat early in a race where I rode wet roads during my warm-up, I decided it wasn't worth the risk of getting something stuck in the tire during the warm-up ride. I swim and run a bit longer in the warm-up to make up for the missing bike ride. Of course, I clean my tires with my hand after every pre-race warm-up ride no matter what the road conditions.

If it's raining pre-race, I normally try to secure a transition spot but wait as long as possible to put the bike in the rack. Agree about putting the run shoes in a bag in transition. If getting cold due to the rain is a concern, don't forget the toe covers for the bike shoes. I doubt this will be an issue at a June race, but I did a race in the rain in September last year where the air temp was in the low 50s. I struggled putting on fingered gloves, so decided that I'd have a pair of neoprene mittens ready for a similar circumstance down the road. Have fun!