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.
I got a
full three days for my senior three day pass. Activated 11am on Mon and expired at 11am on Thur.
Agree that walking often is faster than the DEUCE on parts of the strip -- but for tourists, lots of things to look at from that upper deck. And walking from NYNY to Encore is quite a hike and tiring. I don't think you can get a regular three day pass on the bus (ie. from airport) -- but our bus driver let us ride 'free' to South Terminal as we said we were getting a 3 day pass. But, as I said, can take Rental car shuttle free and walk to South Terminal.
I realize most use cabs - but the bus is an alternative way and your really save a lot of money (it takes longer so less time to gamble

)