Ive been there on a bike twice, its a fantastic country for cycling, lots of people do it, there are officially designated cycle touring routes, lots of good bike shops and bike hire, surfaced roads are all good and many of the unsurfaced ones are cyclable on a road bike. I used 32mm touring tyres.
From Bled there is a great flat trail NE to Kranjska Gora (it runs parallel to the busy E61). After a steep little ride with fabulous mountain views, it joins the main road. At K.G, turn left up to Virsc pass, a true Alpine switchback pass. From here you can roll down to Korabid. The whole circuit back to Bled may be possible but I havent ridden that.
The local maps have lots of detail but occasionally things are in the wrong place for navigating trails.

If you are looking for places to stay you should consider Tourist Farms, they are a way to get into the countryside, eat some typical Slovenian food and chill out.