if you don't own a bathtub, then you can't do a ritual bath. I would suggest maybe asking a friend or parents if you can borrow their's. Otherwise, the only way to really get around your problem would be to buy a bathtub, and I recognise that's probably not the best thing.
you do not need a tub to do a 'ritual bath' have a quick shower. take a dunk in a pool, pond, stream, whatever standing body of water you have around you. is it raining, stand under the gutter flowing with rain water.
If this is an 'ancient' concept, our ancestors did not have tubs either, they bathed in ponds and streams if they bathed at all.
A favorite variation of a ritual shower is to make a 'salt wash,' and to pour it over one's self while in the shower.
Basically, it's just adding things which would have been added to the bath water, into a cup. Warm water is added, and as much as possible is dissolved (you don't want granular salt cascading down your scalp, getting into your eyes or other sensitive areas, trust me!). If herbs are used, then hotter water can be used to help 'steep' them, and they can be strained out, into another container. Of course, oils are generally fine to add!