By now, I'm sure most CrackBerry readers have updated to PlayBook OS 2.0 and have already been through the ins and outs of it all but in case there is anyone out there who hasn't updated yet -- when you do, you will notice there will no longer be a "BlackBerry Bridge Browser" on your PlayBook. It's not something wrong with the OS, in fact -- it's done that way by design as noted below:
After upgrading to BlackBerry® Bridge™ 2.0 on a BlackBerry® smartphone that is not associated with a BlackBerry® Enterprise Server, the Bridge Browser icon is no longer present on the BlackBerry PlayBook.
This is by design as the native Browser provides the same functionality when bridged, therefore making the Bridge Browser redundant.
In other words, when you are connected to your PlayBook via BlackBerry Bridge the browser will use your BlackBerry connection for data usage, unless WiFi is enabled. If WiFi is enabled it will automatically use the WiFi connection associated to your PlayBook. Now, no one has to wonder which browser to use as there is only one to choose from and it will use the appropriate connection.
Source: RIM KB29992