The whole idea of a "modal" is that there is one pop-up, and you can't do anything else with the page while it is open. You need to find some different widget to do what you want. Modals are meant for when the user's attention is to be momentarily diverted to just one thing, while the rest of the page is still visible (though sometimes with reduced visability/blur, etc.)
I don't advise using both jQuery UI and Bootstrap. You are loading two widget frameworks, there are bound to be conflicts, and you are loading frameworks with redundant capabilities. Yes, you can build reduced versions of both jQuery UI and Bootstrap, but think it not worth the trouble.
Pick one!
Maybe Bootstrap panels will give the visual look you want.
Honestly, all you need is a <div> and place a button in a corner for closing. You just need to write a bit of code to have the button hide or animate the div/panel/whatever.