How can I make a BBQ sauce from my dry rub?

You haven't given us much information to go on here, but I'm assuming your dry rub is a mixture of dried spices and possibly sugar.

If that's the case, I would fry some onions and garlic and add the spices (not the sugar, which will burn) to them while they soften. Then I would add the usual BBQ sauce staples - ketchup, vinegar, some water, and the sugar before simmering for a while to reduce and thicken. Put through a blender and sieve and you're good to go - if your spice rub is distinctive enough, it should translate through into a sauce well.

If there is a particular flavour that makes your dry rub stand out, you could add another 'version' of it to the sauce to emphasise it - for example, if you have fennel seeds in your rub, you could add a shot of aniseed liqueur like Pernod to the sauce, or if you have orange zest in the rub, use orange juice instead of water.

No matter the option, the rub will be an accent to the sauce, not a main flavor. So it would be best to envision it that way from the beginning. It's actually a really good way to coalesce the spices you would add to your sauce, so that you don't have to do duplicate work. Just make double the rub you normally would, reserve half of it (PLEASE be sure you do not cross-contaminate it with the meat you are rubbing), and add an amount commensurate to your personal taste to the wet ingredients. This works pretty well whether you're using tomato-, vinegar-, or mustard-based sauces.