Soda and vinegar is an odd combination. Soda is a base, making water alkali. Vinegar is an acid, making water acidic. Together, they make water neutral again, with a lot of pretty bubbles.
Either one can work really well depending on the stuff you need to get rid of. But adding one to the other just weakens it.
Hmm, it seems to me most of those bubbles will happen not where you need them. Maybe if you throw in the base first and the acid later (or the other way around)