In fact, Hornsby recorded two additional album with The Range (both of which reached the top 20) and had three additional top 40 hits before dropping the band to go out on his own. In the intervening years, he has worked as a studio musician, recorded a bunch of albums (his more recent work has more of a jazz-influenced sound) and played with the Grateful Dead.
While Hornsby's videos were played in the 1980's, his low key approach (which is apparent in "Mandolin Rain" below) did not fit in well with MTV target market. Afterwards, his move to a more jazz and bluegrass influenced sound took him out of the mainstream. However, he remains a talented artist who had six top 40 songs from 1986 - 1990.
Cool trivia fact: Bruce Hornsby co-wrote two top 10 hits for other artists -- Don Henley's "The End of the Innocence" (#8 in 1989) and Huey Lewis' "Jacob's Ladder" (#1 in 1987).