Besides using the 109A to the SST and then changing to the DUECE, you can take either the 108 North or 109A North and then change to one of the east-west buses which run along Tropicana (for MGM area), Flamingo (for Bellagio-Caesars etc.) area. Often walking on the strip one can outpace the DEUCE busses, the strip traffic crawls() and each strip stop can consume as much as 10 minutes with people getting on and off.
The passes are 24 hours from the time of activation (first use on a bus) so get a full day on the general day passes and 3 days on the senior passes.

[A few years ago, one could transfer from one bus to another on one fare--too bad that feature is gone.