the "Owner" portion of the Jeep website gives you a digital service history, including the initial inspection. I would imagine completed TSB's would be listed there as well, although I cannot confirm that, as mine hasn't had any done.
They are also supposed to put a sticker int he engine compartment indicating which TSB's are already performed. Run a search for it and the thread should come up.
They are supposed to be listed on Chrysler website in "Owners" area. I found that 2 software updates I had done at the dealer are not listed. Oil changes were listed
Site supporters may be able to get a check on TSBs that have been done on their vehicle from Milous. Try sending a PM to him, with your VIN. He helped me that way late last winter.