Unfortunately, some of them will not even process bulk loaded film. For example, in my experience this applies to the sendout lab for walmart's (Fuji I believe). They simply returned the full cassette, unprocessed.
I think some of the pro labs will process bulk loaded film and return the cassettes, but they tend to be expensive, which kind of defeats the purpose of bulk loading.
If by chance you could get your hands on some once-shot E-6 cassettes (not bulk-load cassettes) you can bulk load by taping the new film onto the stub of the old film. Then it is not obvious to the processor that you gave them a bulk-loaded cassette, and they may process it. (I recently did this at one of the local mini-labs for C-41 processing.) However, in that case I would not advise asking for the cassette back.