You are going to have a wonderful time! I spent 6 nights in Stara Fužina on a solo trip in July 2023, hiking each morning and swimming in the afternoons, and it's one of my favourite travel memories.
The Lake Bohinj region wants everyone to park their cars and use transit to reduce traffic so the options for car free travellers are great! They have tourist buses that start running in June that link the villages in the region and go to some trailheads. There are different transit ticket options depending on the length of your stay and you can buy the ticket/pass at the tourist info centres. I had the Julian Alps card, which in addition to free transit included access to some sights, free boat rides, and discounts.
My two favourite walks/easy hikes (both of which can be done as loops, no transit required) were:
- Through the Mostnica gorge up to the Voje valley and waterfall (https://www.bohinj.si/en/mostnica-gorge-and-voje-valley/)
- Walking the circular part of this route counterclockwise, starting from my hotel: https://www.bohinj.si/en/aktivnost/bohinj-cycling-route/ (shared as a cycling route but I never saw a single cyclist once I started climbing up the hill out of Brod, only walkers). I love seeing all the hayracks around Studor
I also did stage 7 of the Juliana Trail (https://julian-alps.com/en/tour/hiking-trail/juliana-trail-stage-7-stara-fuzina-bohinjska-bistrica/34668333/), the loop around the lake, and, with the help of twisty bus ride to get up a mountain, a longer hike to the Vodnik viewpoint but I wouldn't prioritize any of them for a short trip. For seeing more of the lake, it would be nice to walk out along the north shore and cruise back on the boat.
For swimming, head away from the bridge in Ribčev Laz to find more room to spread out (and fewer day trippers taking pictures of you from their boat tours). The area just north of Restavracija Kramar was great - enough people that I always felt safe swimming on my own, but not too many.
Have a fabulous time!