Not Bayesian, but can't you just do ANOVA w/ the non-summarized time of day vs. open rate (using hourly buckets)? That seems like a good first-pass way of telling whether or not there's an actual difference there. I confess that my stats knowledge is really just from natural sciences experiment-design parts of lab classes, so I have a bias towards frequentist look-up-in-a-table techniques just because they're what I've used.

Rant for a different day, but I think physics/engineering students really get screwed in terms of learning just enough stats/programming to be dangerous. (I.e., you're just sort of expected to know and use them one day in class, and get told just enough to get by- especially numerical computing and C/Fortran/Matlab).