What is "liquid white" that Bob Ross uses?
It's a proprietary product from the Bob Ross company.

There's 3 such basecoats that the company makes: Liquid White, Liquid Black, Liquid clear.

The official description reads: 


  Liquid White is one of three Bob Ross Liquid Basecoats essential to the Bob Ross Wet-on-Wet Technique®.  These basecoats (Liquid White/Black/Clear) allow us to actually blend and mix colors right on the canvas rather than working ourselves to death on the palette.  The Liquid White/Black/Clear can also be used to thin other colors for application over thicker paints.  The idea that a thin paint will stick to a thick paint is the basis for this entire technique.


Bob Ross's mentor, Bill Alexander, used a similar wet-on-wet technique using "magic 
white" as a base, or sometimes called "fluid white". 

It seems entirely possible to make your own. 


  All you need to do is dilute titanium white with linseed oil. Mix these together until you get a creamy consistency. Some artists choose to mix equal parts of linseed oil and Turpenoid (or turpentine) to create this homemade medium.


So, linseed oil and titanium white (paint). I would presume that the quality of the titanium white paint you use will affect the quality of the fluid white you make. 

Since oil paint itself is generally made from linseed oil, pigment, and a binder/emulsifier to get the oil and pigment to "stick", it's likely feasible to make liquid white using pure pigment (titanium dioxide), linseed oil and something like white beeswax.