I don't think it's tacky, but most people will. When I got the invitation, I said to my friend (the mother of the bride) "Oh, that (country club where it's being held) is on a big hill." She replied, "Only you would say that."
It's only about 8 miles from my house, but I do sweat a lot. Maybe if I rode my Jamis, I could go slow enough to not sweat, but I would have to change. I don't know the people giving the shower (groom's family), except they are very ah, unsophisticated people who might freak out if I came in in cycling gear. I also don't want to cause any issues for my friend, who has enough stress with this child and the whole event.
I will try and ride before or after the shower.