I have some expertise here (have used sonar under breaking waves) and I'd say you're spot on. Bubbles act like acoustic black holes, they absorb sound like crazy. Whether you're trying to ping through them in the water, or also if they get stuck on the transducer. The lidar analogy seems apt. The OP speculates that wave breaking noise might be causing interference, but the noise will be way lower frequency than the sonar (ie audible frequencies) so masking by bubbles makes more sense. Any new ideas to mitigate this would be a big deal for sonar!
Also, very cool idea and project!