This is an underrated and under-reviewed experience. On a practical level, it's transportation,…read morebut it's also a scenic byway across Catalina Island - probably than 1% of Catalina visitors ever journey across the Island by Safari Bus.
The Safari Bus, which can be anything from an 8-passenger van to a "retired" school bus will take you on an approx. 2-hour journey between Avalon and Two Harbors (which is approx. 14 miles as the crow flies, but much longer via windy roads.)
So a huge percentage (like 75% or more of the Island is owned by the Catalina Conservancy and is protected from new development. The Safari Bus is the only way I know that you can visit the "interior" (aka Conservancy property) without obtaining a permit (hikers and other can obtain permits for a modest fee in either Avalon or Two Harbors.)
Some of the windy roads on the Island are hairpin turns with little or no road edge and no guardrail. Rest assured that your drivers are natives who could probably drive the road with their eyes closed (they don't) but if you have anyone really skittish about heights, put them in the middle seat :) Along your route, you are very likely to see the bison (non-native, but now so iconic that they remain, albeit on birth control :) and the native Catalina fox (very small and VERY cute.)
Most of the vans/buses will not have A/C, and their shocks are pretty worn. The roads are just as worn, so be prepared for a pretty bumpy ride. You'll pretty much stay under 25 mph, though.
The bus runs Avalon-Two Harbors approx. 1-4 times a day, with a lot of runs in the peak season (late June - Labor Day), and fewer in the shoulder season (spring/fall) and fewer still in winter. It's best to make reservations if it's critical to take the bus. In the summer, buses are regularly full and you might miss out. You can make reservations online through the Santa Catalina Island Company website (they operate most of the touristy things on the Island) or at the kiosk in Avalon, or the check-in office in Two Harbors. The website is (currently) weird. (many things on the Island are!) You have to book each leg separately. Know that the legs are 1) Avalon, 2) Blackjack/Airport, 3) Little Harbor and 4) Two Harbors (or the reverse if traveling the other direction) and you'll figure out which leg(s) to book.
From Avalon, you ride about 45 minutes to the Catalina Airport. Blackjack campground is nearby - if there are campers to be picked up/dropped off, they'll stop here briefly, too (not very common, because Blackjack doesn't have much shade and is not close to the water. It's mostly a stopping point for those hiking the Trans Catalina Trail.)
You don't usually take the same van/bus all the way. One van does the Avalon-Airport leg and another does the Airport-Two Harbors leg. You will disembark at the Airport and have a 20-30 minute wait for the next van. There's a counter service grill restaurant and a gift shop. If you want food, order it right away so that it's ready before you depart. There's some nice seating outside with a great view.
The second van will take you from the Airport to Two Harbors and will usually stop at Little Harbor on the way. The second leg is about 30-45 minutes. Little Harbor is beautiful, remote beach camping on the west side of the Island (see my separate review.) Nothing but firewood and water can be obtained there, so the Safari Bus driver may stop in Little Harbor to pick up passengers, to drop something off to campers, or to take reservations from them (I don't think any cell phones work here.) Little Harbor is especially gorgeous after the Spring rains - it's lush and green and stunning. P.S. There's a separate service that will deliver kayaks and other gear to you in Little Harbor.
Lastly, the Safari Bus has some limits on gear (I think it's two items per person, not including a small personal item.) In the summer, they are more likely to be strict about this due to sold-out trips. It's best to consolidate your gear as much as possible.
Lastly, it's nice to tip your driver(s). Bring some cash for two drivers/each leg.
Enjoy!