Reality but not like this...
Newbie w/ BS and a Level 1 and 2 nailed seeks Stakehorse. Do they really exist? If so, what kind of terms can I expect? How long would such an arrangement typically last?
There are a number of players/teams who will bankroll new players. I've done it myself, though not for card counters. However, they aren't just going to give money to someone who just turns up and asks for it. As a general rule you would want to read thoroughly, get the fine details straight in your head by asking questions on forums like this one, build a relationship with existing players, and gain some experience at low stakes. Then probably you won't even have to ask: a trustworthy competent counter is quite a good financial investment and someone may well offer to bankroll you.
At the moment I think it is very unlikely will take you up on your offer. We do not know you from Adam. You could be a casino guy searching for dirt or a scammer looking to rip people off. Probably you aren't, but people do have to take sensible precautions.
Second, you say you play BS. Although playing your hands according the count isn't actually worth that much in terms of expectation, every serious player still does it and they would expect any one they bankroll to do it too. Also, you mention your count system level. Most serious players don't care what system you play, as long as you play it accurately. It would never be a major consideration, which advertises your inexperience.
Additionally, you need a GC subscription to gain people's confidence, because that tends to weed out some of the wheat from the chaff. I'm not shilling for the site here, I'm just describing things as they are.
You may think I am being harsh here. I am not. You can't be expected to know how the system works till someone explains it to you bluntly.
Stick around here, learn as much possible, be patient and network, and you should be able to get the help you want.