Bluetooth audio sucks. For car streaming it's okay (since it often works in tandem with hands-free phone features (answering with a dashboard button), but it compresses the sound output in addition to its general flakiness.
If you're set on using that amp and want good sound quality, you're limited in your options. What you need is something similar to the now-defunct Squeezebox line, i.e. a cheap mini-computer sitting next to your amp, with analogue sound out, that streams losslessly over wi-fi, not bluetooth. The closest right now is probably a Raspberry Pi computer with an extra analogue output, running the free
Pi Music Box OS (which supports and DLNA and AirPlay, and has apps for Spotify, Soundcloud, Google Music and others, in addition to local music from a harddrive). Here's a
bundle for this setup. It's cheaper to DIY, but it will take time. On the other hand, there are some ridiculously cool setups/mods out there.
It's basically a Sonos system on a budget.
EDIT: Oh, sorry, didn't notice the Discman bit. If you want to go down that road, I'm stumped. You need a laptop or a smartphone for my setup to work properly, and it doesn't really take physical media into account. If you need the old amp and the old discman, I honestly think there's no getting around wires. There are sound boxes that can do what you want (basically mini-amps with built in wifi), but they're prohibitively expensive, degrade sound quality (slightly) and you need at least a sender and receiver, rendering the whole setup pointless.
