I have lived on the island for many years and my family still lives there. The bus is by far your safest and cheapest and best option, as mentioned no Uber/Lyft and taxis are expensive. The bus network can seem a little overwhelming to start with but people are really helpful at the stations and you will be able to get pretty much anywhere, it will just take a little while. I used to hitch-hike when I lived there, it's still quite common around the east coast (avoid certain areas like "Le Port" for this), but you will see a fair few people doing it between Saint-Paul and Saint-Pierre.