If you go:
(I have not actually been to Cactus League spring training myself; this is information given to me by others, including the nice folks at Lookout Landing.)
The Mariners' spring training is held at Peoria Sports Complex in Peoria, Arizona. Peoria is basically a suburb of Phoenix; you'll fly in via the Phoenix airport.
Bubba hasn't gotten a spring training invite (yet); this means he'll be training with the Triple-A team, the Tacoma Rainiers. Bubba is already in Arizona, but minor leaguers don't officially report until March 6, and their spring training games don't start until about March 15. (The Mariners have not released a minor league spring training schedule yet.) So you'll probably want to schedule your trip for the second half of March.
The minor league spring training games are free, and only a handful of people attend. Which could be kind of cool. You'd be guaranteed great seats!
Getting tickets shouldn't be a problem for the big league games. The Angels and Cubs games sell out, and Mariners weekend games may sell out as well. But it sounds like most days, you can just walk up and get tickets, at least if you don't mind lawn tickets. If you want to be sure to get good seats, buy your tickets ahead of time at Mariners.com.
The major league spring training schedule is here. I'll post the minor league spring training schedule when it's released.
You might find this guide to spring training useful. It's several years out of date (the $4 lawn tickets are now $6), but much of the information is still good, especially the recommendations for other things to see and do in the Phoenix area.