There are artists who are or arent't big stars in the general public but are virtually legendary or worshipped by musicians, and Bowie is one of those.

Bowie's music/songwriting had a massive influence on people who were teenagers in the 70s and became musicians in the 80s. It's not just a few bands, it's most immediately almost all the British glam scene, a fair share of the original British punk movement and a large percentage of the new wave scene who credit Bowie's songwriting and experimentations as a direct musical influence (and of course several of them also claim his looks, his attitude, his live performances also influenced them just as much as his music did).

Bowie is one of the few musicians whose music (different periods, of course) influenced such a very wide spectrum of musicians, from A-list pop stars like Madonna to the better known and seminal altermative artists (Joy Division, Bauhaus, The Cure etc.) to all sort of more obscure artists in the underground/experimental scenes.

It didn't stop after the 80s (nor was it quite limited to Britain), a whole new crop of artists also claim Bowie as one of their main influence in the 1990s... (in the grunge scene, in the techno-industrial scene with people like Marilyn Manson and Trent Raznor etc. pop stars like Gaga)

Another good indicator of Bowie's musical influence is the massive amount of cover versions of his songs by artists working in all sort of genres.

Not all his "periods" were as influential though. When he went mainstream pop in the mid-80s that phase was not very influential on musicians, and post 1990 he was more a chameleon, very often collaborating with the new avant-garde artists, but adopting their innovations, fusing them into his own style, rather than innovating himself.