Getting from Tiraspol to Odessa took about 2hr in the bus. The most nerve-racking experience was at the Ukraine border. All of my bags were X-Rayed and I was questioned about several items in my bag and asked where I bought them. The border agent was very interested in if I had purchased anything in Transnistria or had any USSR souvenirs like coins or anything containing a hammer & sickle.

I crossed the Poland/Ukraine border last year and was not asked any questions like this, nor were my bags X-Rayed, so this is definitely a Transnistria/Russia thing with Ukraine.