May in St Tropez--cheaper accommodation possible? e.g. E50-60 per night?
access via boat or bus from St Raphael?
The best way to get to St Tropez is via luxury yacht.
No train station in St. Tropez, so I guess it's bus, rental car or boat.
May isn't peak season on the Riviera unless you hit some sort of special event, but I don't know whether you can find something in your price range in St.-Tropez. I managed to do it in Nice last May, but I only needed a single room, and I suspect hotel rates are lower in Nice. I'd check booking.com to see how prices look. If you find some likely-looking possibilities you can use to Google to locate their individual websites, where you might save a bit of money or get a continental breakfast thrown in for free.
There is a bus from St. Raphael. The best access to and around St. Tropez is by car (or yacht). It's really not a budget destination, but anything is possible with a bit of effort and careful planning. Also look at airbnb, tripadvisor rentals/Flipkey, homeaway, etc if you are staying more than a night or two.
Note the dates of the Film Festival when considering alternatives.