Reddit mentions of Solos for the Double Bass Player: Double Bass and Piano

There's a book called Solos for the Double Bass Player which is an Oscar Zimmerman edited collection. It's got a few good early pieces, and some pieces for you to grow into.

When I was going to school I used it quite a lot in my first year, and every time I play Bottesini's "Elegy" in orchestral tuning, I can conveniently just give my accompanist that book, because it has the accompaniment in the right key. It's a good buy for that reason alone, frankly.

Other fun starters are around - "The Elephant" from Carnival of the Animals is a great early piece that allows you to focus on musicality without a huge level of technical difficulty.

If you want a growing challenge, Dragonetti's 12 Waltzes for Double Bass solo are super idiomatic to the instrument, but have a good level of technical challenge in addition to their musicality.

As for high level pieces, some people worship the Cello Suites. I differ, and think they sound very bad on the bass (and that's me using my most politically correct language on the subject). However, they do present a useful technical exercise if one really is determined to play them. They require a lot of extended technique and creative fingering choices, so they're good for making you "think with Portals". As an alternative I would recommend the Weinberg Solo Bass Sonata (which is written in the style of the Suites, but not the harmonic language) or the Fryba Suite in the Olden Style. Both were actually written for the bass, and are much more musically rewarding to complete.

My Recommendation? Start with the Elephant. if you find it too easy, buy the Zimmerman book. Once you get bored with that book, try out the 12 Waltzes, then branch out from there.