Grounding the bridge does the following: when you touch the bridge or the strings then your body acts as a shield to extraneous noise fields.
The potential danger is that this creates a shock scenario is if
- there is a fault in the amp placing a high amount of voltage on the chassis (to which the strings are connected via the guitar cord),
- the wall outlet your amp is plugged into is improperly grounded and you touch something properly grounded or
- the wall outlet another band member uses is improperly grounded and you touch each other.
See more under
www.guitarnuts.com, re. shock hazards.
If the pickups have covers and the control cavity including the output jack are perfectly shielded then the string ground connection is not necessary. It is not a failsafe measure though - you still can be shocked when you touch anything connected to ground such as dome speed knobs or pull the cord out of the output jack.
Best to keep equipment in good shape, have the amp's ground connections regularly checked and check the outlets used at each gig. I always checked at gigs with a multimeter whether there was any voltage between the strings and the microphone.
Cheers Stephan