The bass part in "Hound Dog" varies a little bit from verse to verse, but it's something like this:
While the tonality is different, many bass parts in Zombies songs also have this sort of dotted rhythm. For example, here's the bass part in the verses of "I'll Keep Trying":
(There are a couple measures in the chorus that I'm a bit unsure about, but otherwise, the entire bass part in "I'll Keep Trying" exhibits this initial pair of dotted quarter notes in each measure, save for the last bar.)
The bass part in the verses of "If It Don't Work Out" also has this rhythm for all but the last two measures, but since there are nine consecutive measures of nothing but D notes, I felt an excerpt of the notation wouldn't be very helpful in illustrating my point.
More often, however, there's a slight difference in the rhythm in that this single quarter note is replaced by a pair of eighth notes, which sometimes precedes the dotted quarter notes and acts as a pick-up.
For example, the beginning of "Whenever You're Ready":
The beginning of "Time of the Season":
And the verse in "Tell Her No":
(These parts may show the influence of Ben E. King's "Stand by Me" more than Elvis's "Hound Dog," though. As I pointed out before, albeit imperfectly, so I won't link to it, these bass parts share the same rhythm and the same tonality as "Stand by Me": root, fifth, and seventh.)