I filled out our application online about a month ahead of time and wrote down the reference number. Like previous yelpers mentioned, I recommend that method to everyone.
There were 2 lines when we entered, 1 for online applicants and 1 for walk ins. The walk in line was about 3 or 4 deep on a tuesday morning, while our line was wide open. After waiting a minute for the next available receptionist, we were on our way to getting our marriage license. The woman explained everything in detail what we needed to give the wedding chapel and how to order a copy of the certificate online afterwards. She was very nice and helpful. The whole process took less than 10 minutes. Quick and painless.
We took the SDX bus from Mandalay Bay to Bonneville Transit Station stop and walked around the next block to get to the bureau.