If you are a male, and you exit a communal taxi (mashrutka) in front of a woman, it is considered necessary for you to turn around and offer your hand to hold while she exits. This seems to be the custom for most of the Soviet Union. While i rarely saw anyone give up their seat to an elderly person, or a woman, i got a very negative reaction the first time i failed to offer my hand.
There are several possibilities to reach Trans-Dnjestr/Tiraspol. You can take a train (Route Chisinau-Odessa, but is often closed when Tiraspol disagree with Chisinau in a certain issue) or a bus (check the main bus station) from Chisinau. We decided to take a taxi, so we will have no problems to get back at the right time. If you pick a Taxi watch out for the Trans-Dnjestrian plates. It's easier to go with a taxi which is driven by a Trans-Dnjestrian.
Make sure the driver understands when and where he has to pick you up.
While modern cars and old buses ply the streets here, this tends to be the prefered method of transportation for some of the locals. You will also see this in the rural parts of Moldova.