Naturism and topless on Barbados beaches
In Barbados it is generally not allowed to be fully naked or in case of women to be topless on the beach or in public.
Nudism and topless for women is not allowed in public. In general topless women are usually asked in a friendly way to cover themself up, if anything happens at all. You will probably see some women who are sunbathing topless.
But despite that, it is prohibited and especially the older generation of Bajan's are very traditional and religious. So please respect and follow these rules and regulations.
Topless on public transportation
Bare-chested people - whether a man, woman or child - who wants to use a public transportation will probably not get very far. For example, bus drivers will usually don't let you in the bus. This has solely hygienic reasons.
Alternative for streak-free tanning
There are some UV transmissive beachwear on the market. I cannot tell you how good it works because I never tried it but you can search for it on google.