Hey Chris! 3 weeks? Lucky is right! Are you thinking about JUTA or route taxi's around the island? That would be very adventurous for a single lady. I've known people who've done it with a hired driver. Typically that's a 3-4 day trip with a driver running on your schedule and a lot of car time. Don't know anybody who's done it on the public transport. Don't know how long it would take on public rides. Do A LOT of research if you're serious about it. Have plans, alternate plans and emergency plans. Good luck!
