Only done pootling on a hired MTB in Slovenia, in both directions out from Kranjska Gora (up in the north-west of the country). Took trips into Italy (Lago de Fusine and Tarvisio), and in the other direction to Jesenice via Mojstrana and it's Slovenian Mountaineering Museum and a nearby waterfall (though I could have continued on to Bled had I not done Italy in the same day).
They have some fabulous segregated cycle routes, which are usually well away from any roads and go through the countryside. There are frequent picnic tables and taps to refill bottles en-route along these paths, and often enterprising farmers have opened little cafe-stops on their land next to them.
Kranjska Gora is an alpine area, so there are lots of climbing opportunities if you have the legs for pretending you're doing a mountain stage in the TdF. You can head up the Vrsic Pass and onwards to Bovec, or try the Wurzenpass from the nearby village of Podkoren over into Austria.
Ljubljana, the capital city,is an extremely bike-friendly, cycling city. Lots of racks of hire bikes, lots of cycle lanes and lots of people on all manner of bikes.