Instead of grounding myself with a bracelet, can I wear rubber gloves? Will this prevent any equipment I touch from getting shocked?
The best way to prevent static shocks is not to try to prevent static discharge, but to ensure safe discharge. Otherwise the charge will just continue to build up until it finds some (unwanted) way of discharging.
Many labs ensure this by using shoes with conductive soles, and a floor that conducts to ground (no pun intended).