There is some fantastic fishing to be had in Slovenia, particularly for those who enjoy fly fishing.
The most local river to the house is the Sava Bistrica which has large rainbow trout, brown trout and grayling. The river is stocked but also holds a good number of wild fish. The fishing on the river is divided into three sections between Bled and Lake Bohinj and you will need to buy a permit for each individual section. Permits can be bought at the fishing shop in Bohinjska Bistrica, or Fauna Bled below the Panorama Hotel in Bled. Fauna is run by Matej who is a real fishing expert and a great source of knowledge. He also ties some beautiful flies!
The other local river is the Radovna, which is smaller than the Sava Bistrica but runs through a very beautiful valley down towards the Vintgar Gorge. The river is unstocked and holds some lovely wild brown and rainbow trout. Permits can again be bought in both of the shops mentioned above.
There is also fishing on Lake Bohinj (not just fly fishing) where you can catch trout, grayling and lake char, as well as other coarse fish.
One of the biggest and most popular fishing rivers in Slovenia is the Soča, in the next valley over the mountains beyond Lake Bohinj. This holds some sizeable rainbow and brown trout, as well as marble trout which are native to Slovenia and can grown to be very large. There are a number of other tributaries of the Soča including the Bača and Idrijca, which are both very beautiful and hold some excellent fish. To access the Soča, the easiest way is to go on the car train from Bohinjska Bistrica which goes through the mountain to Most na Soči. The journey takes around 40 minutes.
Further afield, there are a number of other wonderful rivers in Slovenia, including the Unica, a real gem of a chalk stream further south towards Postojna (around 1.5 hours drive), and the Krka (towards Nova Mesto). For further information on fishing in Slovenia, your best bet is to drop into Fauna Bled and talk to Matej.