What does the phrase "taking a bath with the crowd" mean?
Solution 1:
Stéphane's suggestion, “to mingle with the crowd”, may well reflect the intended meaning of the speaker of the phrase. But note that in English, the phrase “take a bath” often is associated with a stock-market loss (1, 2); since the European idiom is not well-known in the U.S., I'd expect American English speakers to either associate your phrase with taking a loss in the market (along with a crowd of other investors) or to interpret the phrase literally.
Solution 2:
It means “to mingle with the crowd” or maybe a bit more faithfully to “immerse oneself in the crowd” (as suggested by StoneyB in the comments).
The original idiom is closer to “taking a bath of crowd” (in French at least). Just as if the world were a container filled with human beings.
Solution 3:
It means "to suffer (take a bath) by doing what the crowd is doing" (in stocks, real estate, tulips, whatever). In my book, "A Modern Approach to Graham and Dodd Investing," I noted that every few years, lemmings will gather in large groups, "travel," and "upon reaching their destination, they will all jump into the sea, and of course, drown." The consolation for the fact that they all die is that "every lemming that dives into ocean gets to retire in the same style as every other lemming that does the same."