When I say melodic in this instance I mean clearly less interested in chops, having a voice more in a folk/ambient/free/new music sense. Someone who uses space in a relaxed and thoughtful way, somewhat detached from the usual role of the bassist. The players that come to mind for me are Charlie Haden and Thomas Morgan. Who are some players you dig who have a similar element to their playing? *Feel free to include any electric players. One I found about lately is this guy in Sweden named Gustav Broman, he plays a cool Hofner hollowbody with a real acoustic sound.
My favorite is a portuguese double bassist named Carlos Bica. One of my favorite musicians, favors space and melody. I know him personally and he's a great guy.
Red Mitchell. He is one of my favourite players, and played the first solo I transcribed "What Is This Thing Called Love?" From a Hampton Hawes Trio album. Very melodic and even contains a quote from "jeepers creepers". I have transcribed a few more including some from " Presenting Red Mitchell" and I recommend doing so, particularly the Hampton Hawes stuff. George Mraz is great too, I transcribed "Confirmation" from Eclypso by Tommy Flanagan, cool solo getting round those changes. Ray Brown is very often great, his solo on "Stella By Starlight" from Ray Brown's Walk On is particularly melodic, recorded not long before his passing showing that he remained great right up to the end and also the first solo I learnt to play on Double Bass.
I have recordings where Jay Anderson, Scott Colley, and Matt Brewer all do the thing you described in your original post.
Mannn thanks for all the replies everybody, I'll be busy checking all these folks out for a while! I hope anyone who sees this in the future will keep adding to the list, there are some great players in here!