Havent been on a train in 3 years but as a general rule both overnight and express trains have bathrooms.
the large motor-coach luxury buses such as the ones from Kyiv to odesa also have bathrooms and sometimes working wifi and are about 40 bucks. I took one last year from kyiv because my car was in Odesa.
Ive often paid taxi fare for girls because its just not that much money to fret over. Of course most girls I know arent trying to scam me either.....
It's best to avoid agencies unless you have a clue what you are doing and can read people. If I avoided agencies I would never have met my wife. Agencies aren't magical. Your money status in your pocket till you take it out