Well...no. As the most group-oriented quadra, we carpool any time we have to use a vehicle. But more to the point, it’s typical for ESEs to rather walk, fat and chortling, giving out small gifts of candy and such to children in their paths.
You’d get access to the Alpha hive though. It’s carved into a cliff wall by the labor of enslaved Betas taken during the War. It’s always full of food, drink, and cheer, and your room would be in a tunnel directly above the dining hall (which is, of course, open 24/7.) The SF recreational quarters have hammocks, TVs attuned to Hart of Dixie and cooking shows, and there’s a local media server with a repository of over 23,000 slushy romance and comedy ebooks you could peruse.
As to work, you’d probably be assigned to housekeeping, kitchen staff, or diplomacy, and of course there’s a draft in cases of emergency. But it’s pretty light work; don’t worry — 6 hours a day, and you can set your own schedule, with as many breaks as you like. Your retirement would basically be freedom from chores, and a modest stipend should you ever wish to leave the hive for some reason. People have a tendency to go on cross-country road trips to camping spots, and you’d have a lot more free time to do that as an unemployed geriatric.