I only suggested BHUNP because I associate TBBP with the older LE Skyrim and from some passing article I read while researching something or another implying it was related to the UNP body type. I thought maybe you were coming to SE from LE or something...
CBBE is fine. And if your system is relatively new (ie a system purchased withing the past year or two) 3BBB or 3BBB Advanced depending on where you want to go with skyrim.
For bounce, you need to use either CBBE phsyics or CBBE special when building the player body, and afaik, you'll also need to have a female player. (at least I haven't personally chased and bouncy stuff for my male player...)
I'd recommend that you look around Nexus. for bodies that means using the mod search bar and typing in CBBE, then finding the CBBE mod and reading up on it in its description tab and in the posts tab, or for 3BBB or 3BBB Advanced, doing the same.
Same goes for Sinful CBP, HDT, etc. I can't offer a paint by number solution for you. While in some cases folks in the forums who answer questions might be able to offer a pointer or even a solution to a specific problem on occasion, you really "have to do your own homework" to gain a working understanding of fundamentals. Nexus offers a ton of info on the various mod pages for the different mods. AL it takes is your investment in learning by reading the already existing material.
Please ignore my comment about "controller" and Sinful CPB. That's probably a bit technical for this discussion, at least for most gamers. (PI or PID controllers are the underlying program coding that makes bounce work...)
Presuming you installed the correct version of SKSE for Skyrim SE (instead of the one for LE)...
Afaik, you need several things to make bounce work properly in Skyrim SE
1) a suitable skeleton - XP32 Maximum Skeleton Special Extended - XPMSSE is considered the standard
2) Bodyslide and Outfit Studio - for building your player body and for fitting clothing/armor
3) A suitable body - CBBE, 3BBB, 3BBB Advanced, or BHUNP, depending on what you want
(use the search bar from https://www.nexusmod...ialedition/mods for each of the above and read up. As I noted, CBBE is fine, but read up on the 3BBB anyway...you *might want it instead...idk that's up to you... But Stock CBBE is a safe starting point)
4) The HDT framework. - you'll have to read up on this but briefly, it provides some physics coding that works on "collision" and other things associated with movement (clothing for instance, that moves ~naturally~ in response to player movements) (if you aren't familiar with any of this, again, you need to do some homework. I can't spell it all out for you)
5) Sinful CBP - the mod that controls bounce.
Beyond that, it's all up to you spending the time to learn, by reviewing mods and reading their description and Posts tabs, Chasing rabbits in google and bing searches, experimenting, etc.
I'll be honest, I have no idea what's wrong with your installation. You might have installed LE mods, the LE version of SKSE, you might have mods installed that are fighting each other, etc etc.
My gut tells me to tell you to start from scratch and install only the stock game, make sure it works, then add the SE version of SKSE, make sure game still works, etc etc...slowly, carefully.