Accidents, such as the bus, will happen in any port regardless of who is sponsoring the excursion and regardless of any actions the individual may take.
As far as personal safety, though, passengers should always stay in a group. Females should always be in the company of males (not trying to be sexist here, simply stating that a female(s) with a male(s) is a less likely target).
Most thieves are after targets of opportunity -- no witnesses and easy to get bags and packages -- deny them. Keep your bags under your physical control (bags in front, wallets in front pockets or other hard to get to area), keep your cash distributed through several spots on your body (pockets, socks, shoes, or anywhere else your imagination lets you). Have friendly witnesses (other passengers) with you or very nearby.
Lastly, don't get so caught up in your security that you forget to have fun. Most of those "mean, spooky natives" are simply laughing at your funny shorts and Hawaiian shirt