The bridged version uses a 64 bit auxiliary host. All 64 bit programs can use the full available amount of memory. However, the plugin itself remains 32 bit, so it only sees at most 4 GB of RAM (a little less actually).
Supposed you are on a 32 bit system with 12 GB of RAM and have two 32 bit plugins, A and B. Let A use 1 GB of RAM, then 3 GB will remain for B. On A 64 bit system with 12 GB of free RAM both plugins, when bridged, will have 4 GB available.
Regards,
Steffen