The problem with the idea of burning a BD is that to play as a BD music disc the disc must be "authored", which means all the files must be encoded (not necessarily compressed, though) into a format with a means of navigation - the menu, similarly to making a video DVD or DVD-A. That requires BD authoring software. My only experience burning BDs is using Final Cut Pro, which is Mac only, and I have to say given may more extensive experience authoring DVDs, FPC is quite limited. I've never tried what you're attempting, I don't think FCP would be optimal though.
Real BD authoring software is expensive and complex. Sony just discontinued DoStudio Authoring, which could have done this (again, it's a pro app, not easy). Pro applications like Sonic Scenarist ($5k) will do the trick, but clearly not in budget. Perhaps there's a consumer solutions, but I didn't turn one up in a few minutes of googling.
Two suggestions, the first is cheap and easy. Grab yourself a USB Flash Drive. Get a good fast one
like this, it's cheap to try. Copy all your files to it, you might put all CD tracks into a directory/folder, tracks numbered in order. Stuff the Flash Drive into the USB port on the front of your Cambridge player, see how it navigates all of that. You may have to adjust how you copy files, etc. If you rip your CDs correctly, and end up with files the player can recognized, this will likely do what you're after.
Second idea is a bit more expensive, get a BD burner and test-burn a data disc with the files on it like you did for the Flash Drive. Many players will read data discs and navigate them via a generated tree-menu. It won't be as elegant looking as DVD-A with menus etc., but may work.
However, clearly you're already dealing with audio on a computer to burn discs. Because of that, and for simplicity and convenience of use, I strongly suggest looking into keeping all your audio on a computer and using PLEX to serve it to a playing device. PLEX makes it easy to navigate your entire library, includes cover art and track listings, etc. PLEX is a media server application, so it can do video as well, and navigation is through your video display. Players are cheap/free, and you already own one! The Cambridge will play media served by your PLEX server. PLEX is free, capable, and easy to set up. It can run on any computer, Mac, PC, Linux, and is not a demanding application. In use, you'll never handle a disc again, and have original quality audio.
https://www.plex.tv/downloads/