What is best way to caulk this improperly installed bathtub?
It looks like this is a tub that is not meant for installation up against a wall.   Though it's hard to tell from the photo. Looks like a drop-in tub.  Tubs that are meant for installation along a wall have a flange (not a lip) that the backer board goes over.  This is what actually keeps the water in the tub.  If this is purely a drop-in, you'll want to replace the tub at some point, because you will have leaks no matter how well you caulk (I'm assuming you're using the tub as a shower too).  There are some manufacturers that make non-integral flanges for their drop-ins, but they aren't ideal.  

To caulk the gap, find some caulk backer that will fit into the space.  They are made of foam and come in a variety of sizes.  Put the backer in neatly, and then caulk over the backer.  Use silicone caulk, making sure everything's bone dry before application.  I like to use a caulk tool to make things neat.  I see you have masking tape up, which is a good thing.  Carefully remove the tape right after you caulk, before it sets.