We will be staying in Ljubljana for 3 nights in June. Arriving on a sunday from Italy. We will not have a car. And hope to do a day trip to Lake Bled - maybe by bus?
We would prefer staying somewhere near the old town. Maybe a B&B? or small apartment or small hotel.
On our departure day we will be travelling to Zagreb by either train or bus.
I have looked at Tripadvisor, but any suggestions would be appreciated.

Consider this one

http://slamic.si/

dug_otok thanks for your suggestion. I had read a few trip reports recommending the Slamic. It does look good. It is available for our dates at this stage.
But I was wondering if there are some other options/recommendations as well.

We stayed at the Grand Hotel Union in 2014 and were very happy. Clean, excellent location, big room, great breakfast and fair price.

The Grand Union Hotel does look nice. Maybe a little pricey? But great location.

We've stayed at Hotel Cubo. Great location, helpful staff, nice facility, and excellent breakfast. https://www.tripadvisor.com/Hotel_Re...la_Region.html

The tourist information centre near the river will be able to give you options for day tours to Lake Bled

I really liked the Adora, bu it is at the far end of the old town.

https://www.tripadvisor.com/Hotel_Re...la_Region.html

Thanks for the hotel recommendations, they both look good.
Northie thanks for the location of the tourist information office. Lake Bled is on our to do list.