Bermuda is a lovely destination combining both a European and tropical flair for a truly unique experience. I wouldn't stay away for lack of a timeshare trade.
When we visited Bermuda, we found a short-term, fully-furnished apartment rental that approximated a low-end timeshare. Although spartan, it met our needs with two bedrooms, kitchen, living room, and bathroom. Included was a pool, hot tub, and laundry facilities as well.
We spent most of our time away from the apartment visiting the gorgeous pink sand beaches and historic sites.
A word of warning: Bermuda is an easy destination for New York-based cruise ships. Sometimes you need to time your beach visits to avoid the deluge of cruise ship passengers. There is literally no spec of unoccupied sand when a cruise ship descends on a beach.