An after-party is such a fun bonus event for close friends to keep the celebration going after the reception comes to an end. It's an especially wonderful option for couples that have chosen to host their wedding at a venue that closes early because of noise restrictions. Whether or not to keep the bar tab going at this point is totally your call, but here are a few things to think about in making that decision.
Consider the setup.
If your after-party is at a bar where other people (non-wedding guests) will also be hanging around, it's not necessary to keep the bar entirely open. However, if the after-party is at a private venue where the bar bill has to be kept under one tab, you should probably plan on footing the bill. If you're headed to the hotel lobby, it's a nice gesture to cover the tab but it's not at all expected or assumed.
How to keep costs low.
If you decide to host your own after-party and have it at a private venue or in your own room at a bar, restaurant or hotel, you can always pre-specify types of liquor to be used or order a few pitchers of cocktails in advance. If you're hoping to keep costs low, you might opt to provide beer and wine only. Alternatively, you can do a hybrid where you provide a few pitchers of margaritas and beers on the tables but if guests want tequila they can order their own at the bar.
Someone else may decide to host the after party.
It's not uncommon for the groomsmen or a couple of other friends to step in and host the after-party, thereby footing the bill. While it's not something you can really depend on as far as budgeting goes, it's always a nice gesture that's certainly worthy of a thank-you gift post-wedding.
Be communicative with guests.
A lot of people don't think to bring cash to a wedding and if you know your after-party venue will be cash-only, you'll need to find a way to let guests know. This is something you can mention on the wedding website or casually mention to a couple of friends verbally and ask them to spread the word. Maybe say something like, "We'll have a few pitchers of margaritas on the house at the after party, but if you think you'll want shots or beers, be sure to bring a stash of cash. Ye Olde College Inn still hasn't upgraded to accepting credit cards."