How do I participate in special nights?

You can take your sim into CAS through the mirror or dresser. Once there, set up a bear or knight costume as one of their everyday outfits, 3 or 4. On bear night, have your sim change into the outfit and send them to the bar.

Do we know if it’s possible to change the nights? Ie if I have a bowling club can Tuesday be bowling league night?

Hello.
This is a list of the special bar nights and the days/theme in case it may help you.
http://simsvip.com/sims-4-get-together-guide/#BarNights

Just use mirror or dresser. And also make sure, that you have Outdoor Retreat game pack, or there's no bear costumes.

A belated thanks to everyone who answered :)

"MGSFan612;14607683" wrote:
A belated thanks to everyone who answered :)

You're welcome :) I hope that your sims will enjoy attending the special bar nights,

Sometimes people call my sim for alien's night and I'm pretty sure you can't even disguise as an alien. I always think of my sim declining and saying: ''Do I look like an alien to you!?'' or ''What are you trying to say here!?''. Hahah.

"PerfectSorrow;c-16667827" wrote:
Do we know if it’s possible to change the nights? Ie if I have a bowling club can Tuesday be bowling league night?

I don't think so because Get Together came out before the Bowling SP.