If I have been doing my weekday job - sitting (or standing) at a desk, in a climate controlled environment - all day, I do not shower before I get in my hot tub.
If have been doing "weekend stuff" - cutting the grass, DIY projects, hiking, basically working up a sweat in some way or the other - then I do shower before getting the hot tub, but then I shower after that regardless of if I plan on hot tubbing.
We do have a dedicated pair of suits for the tub. Au naturale is not an option for us, unless the neighbor wants a show. We (my wife especially) has found that our hot tub tends to destroy suits. It messes up any fabric that has elasticity. So we just use the same old suit over and over again for the hot tub, and just let them dry between uses.
I don't shower after using the hot tub, but then I am a shower in the morning kind of person - it helps me to wake up. When I used to run a lot, I would get up, shower, go out for a run, and shower again before work. I needed the shower to wake me up enough to actually have a productive training run.
My wife, on the other hand, is a shower at night before bed kind of person, since she is out of the house around 6:40 AM (I work from home most days and start 7:30 - 8:00 AM, whenever the shower and coffee kicks in) so she often shower after using the hot tub, since we normally use it in the evening.