CMYK values are based on whatever CMYK profile is currently accessed to build that mix. Sounds like the two products are using different CMYK profiles and calculating them from the same RGB values.
A quick bit of testing shows that your Photoshop setting for CMYK is USWebCoatedSWOPv2 - a pretty good middle-of-the-road profile.
The build from Color Bridge is using a very heavy black generation - probably a lowest-common-denominator approach Pantone uses to give the most consistent color in the face of inevitable press drift in most assuredly unknown press conditions. A crapshoot.
The actual color that comes off a press from a given CMYK build is very dependent upon paper and press conditions.
Tread lightly here when recommending a CMYK build to your client. Include a BIG caveat.
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I agree, but I think it's best to go by the actual Pantone Solid-to-Process swatches or Bridge which has been updated and looks to be the most reasonable mix for process color. There really isn't any need to get into caveats, though. The client needs the industry standards and those can be found in Pantone's swatch books. The problem with PS is that, the numbers do get affected by the Color Settings in the application, whereas the Pantone Bridge swatches are actual printed samples of the closest they could come to 549C and a standard print industry expectation.
Thanks to all for your help!