I don't think it's wise to pay a company to let you work for them. I'm a rather skeptical person, and I'd be leary of anyone taking my money in such a scenario. Seems like a good way to lose $10K and wind up in the same place a few months later.
You haven't said what you've done to try to get a job. You should talk about that before people can give you advice. I have nothing to go on there, so take this with a grain of salt.
Did your bootcamp give you a promise of any assistance in finding a job? Have you kept in touch with any of your cohort? Reach out to them for help (explain the problem, ask if they have ideas that could help). These are two things that I'd try, right off the bat.
As someone else mentioned, talk to several recruiters. Present your resume and see what kind of feedback you get. If they tell you that they will be unable to place you, ask them if they think you don't have enough experience, and what they think you are missing. Recruiters are not your friend, but they are in the business of making money by placing people in jobs. If they think that they can make money by putting you in a job, they will try to do so.
Next: NYC has a smorgasbord of tech meetups with free or low-fee entry costs. Go to as many as you can. Most such meetups have an initial 30-minute period when you can stand around and talk to people about their jobs. Take notes, then go home and use the Internet to find out more about the parts of these discussions that you didn't understand. This should help to make you more technically competent.
Next, you want to do some "informational interviews": https://en.wikipedia.org/wiki/Informational_interview
If you have friends, friends-of-friends, relatives, etc. who are working in an area that interests you, tell them you'd like to spend 30 minutes or an hour to ask about what they do at their jobs. Keep in mind you're not going to ask them for a job. You're just asking for information. Take good notes, bring them home, and again research the parts that confuse you. You can do phone informational interviews if needed, too.
The informational interviews and tech meetups are intended to help you build a network of people who know you, know that you are looking for a job, and may be able to refer you to an open position. They will also be a goldmine for learning more about the field that you want to break into.
It may help to build a small side project, and have some code samples in github. I can't speak to that, since those things never helped me.
Good luck!