My sports bi-retro says hello. IMO, the feature on the watch is not just the jumping hour. It is also the retrograde minute hand on yours and on mine, also the date hand/s. If you have handled the the watch, you will have noticed the minute hand does not make a full turn clockwise but when it reached 60 mark, it swings anti-clockwise back to 0. It was this feature that made me purchase the watch more than the jumping hour. The movement on mine is a Girard Perragaux calibre 3300 which is a trustworthy workhorse. It could be the same on yours. If it is not, I am quite certain it is still a GP movement.
As you mentioned, the case is quite thick as there is an added module for the retrograde system on top on the GP calibre. My watch is in a titanium case but it is one of my heaviest watches. I was surprised when I first handled it as I had expected a lighter weight. However I think yours is a ladies model at 35mm. Mine is around 42/43mm. I may be wrong though.
You have have reservations about servicing the watch after Bulgari bought over Gerald Genta who was in turn bought over by LVMH. LAst I heard, Bulgari will still be servicing the Genta watches so I guess no worries about that. I don't follow the preown prices of these watches so I can't advise much. Anyway here's a couple of pics of my Genta.
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