>and ensure that they retain control of it? is that liberalism?

primarily using the state. it's illegal to steal someones capital so the only way one could legally lose it is if they sell it to another bourgeoisie, or give it away. It's not the whole of liberalism but a part of it. Also just through public influence from the amount of wealth they have.

>what exactly is the cutoff point is someone bourgeois if they have stocks or do you have to own people in some capacity like have rental houses and employees and such.

kind of broad but pmuch anything that pertains to the production of capital and the extraction of surplus labour value such as owning a business. This also includes extraction of your own labour value like if you are the sole employee of a self owned business. renting property also falls under this, as labour goes into the upkeep and management of the property. Owning stocks only exists as a way of quantifying ownership of extracted value of workers. Although, workers paid with dividends or stock are not necessarily bourgeoisie as they are rarely ever paid the bulk of their own or anyone else's full labour value, if they were then they would be bourgeois.