For a bedside player the necessity for switching out discs, plus the bulk, might make using a standard CDPlayer (or universal disc player) problematic, given you have other options. I use an old Marantz CD60 but that's because I had it in my main rig before I got into using headphones, but if I didn't and I needed a bedside rig now, there are lots of other options.
For about $400 and assuming you already have an iTouch or iPhone, there's the Pure i20 digital dock, and you can pair this with an Ibasso D12 with the former sending out digital signals to the other. Or if the CS4392 on the Pure i20 is enough for you, you can just spend $99 on that and then about $150 on a Little Dot 1+ hybrid tube amp. Or you can get the QLS QA350 for $200 and maybe you might be content not using a separate amp and DAC.
If you can wait for the Fiio X3 though, it's a lot like the QA350 in a pocketable (not to mention more fashionable, less-DIY looking) form factor; both use the WM8740 used by many standard size CDplayers. In case you need an amp that has the grunt of the LD 1+, you can dock the X3 onto the E9, or if you prefer, use a DAC+Amp or separate DAC and amp. In any case depending on the size of any DAC and amp you will use these will typically use less space, just be careful about falling asleep wearing the headphones as these are light enough to get dragged off the table.
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Although if you really prefer the traditional CDPs, I'd recommend Marantz. The headphone drivers are decent enough. Tascams are good too and they don't look too "pro", ie, bright buttons that are easy to find in studios or concerts are an eyesore at home.