In my experience, it's not possible to walk around Bassenthwaite Lake, or Bass Lake as we tend to call it. There are a few places on the east side of the lake, where it's possible to walk near the water, but most of it is either private land, or too wet and boggy.
The nearest fells to Castle Inn are Binsey, Ullock Pike and Dodd. It would be possible to walk to Binsey, but a large part of your walk would be on roads. A walk, taking in Ullock Pike, without using a car would take you a lot more than 4 hours and it involves a very steep climb. Not sure if your partner would like it though. Dodd would be Ok to do, but you'd have to drive to it and pay to park in the Dodd Wood car park.
My suggestion, would be to do Sale Fell, which is a lovely little fell on the north west side of Bass Lake. I live close by and Sale Fell is one of my favourite walks. You would have to drive to it, but it's not far from the Castle Inn.
There's lot of variations of this walk, but the most popular route starts from the parking area near on the Wythop Mill road. If you want a longer walk, you can park on the road opposite the Pheasant Inn and walk up the road from there. The views from the summit of Sale Fell are stunning. I live close by and Sale Fell is one of my favourite walks.
Here's a link to the Walks Lakes website, showing the route and some photos:
https://www.walklakes.co.uk/walk_150.htmlAs I said, there's lot of variations of the Sale Fell walk, some of which that go through Wythop Wood. I haven't suggested those because all of Wythop Wood is closed for tree felling for the next few months.
Let me know if you need any more info.