Thanks for posting this. As a retired trombonist, I find these Fillmore pieces always interesting. I don't suppose the label identifies the trombonist(s) that we're hearing?
Some historical background:
Miss Trombone was one of a series of trombone solo pieces, of which
Lassus Trombone is probably the most well known. Others had titles like
Teddy Trombone, Boss Trombone, Bones Trombone, etc. Some of them, like
Lassus Trombone and
Bones Trombone, were based on racial stereotypes: for example, the subtitle of
Lassus Trombone was "De Cullud Valet to Teddy Trombone." The sheet music cover, as published by Carl Fischer, showed a caricature image of a "cullud" trombone player dressed in tails and outrageously large shoes. Carl Fischer republished the complete series of The Trombone Family, collected in a single volume, some years ago; in this new edition, the obvious "darkie" features of Lassus were bleached!
All of these pieces are, in form and style, ragtimes. They came with piano accompaniment and were also arranged for band, as in this example. Henry Fillmore (1881-1956) was a prolific American composer of band music. See
https://en.wikipedia.org/wiki/Henry_Fillmore for a concise biography. There's also a reproduction of the cover of
Lassus Trombone in the article.
The technical term, taken directly from the Italian, for the trombone "smear" is
glissando (literally, "sliding"), and among musicians is always referred to by that term. Few instruments can perform a true glissando, among them trombone, unfretted strings, and pedal timpani. Keyed and valved instruments must fake a glissando by half-valving and -keying. A good example of a faked glissando on clarinet is the opening of Gershwin's
Rhapsody in Blue. Louis Armstrong was a master of the faked glissando on cornet/trumpet.