Bonnie Bess is a typical example of 19th-century American salon music meant for domestic enjoyment. It uses arpeggiated figures to provide a warm, harmonic backdrop for the primary melodic line.
Balance the arpeggiated accompaniment carefully so it does not overwhelm the melodic contour.
Comparable difficulty and character — good candidates for what to learn next.
Bonnie Bess is rated Henle level 3 of 9 — late beginner repertoire, roughly ABRSM grades 4–5. In the RCM system it corresponds to about level 4.
You should be comfortable at Henle level 3 — meaning you can already play level 2–3 pieces cleanly. Learning it one level early is possible as a stretch piece, but more than that usually leads to months of frustration.
A typical performance of Bonnie Bess lasts about 3 minutes.
Bonnie Bess is available as free public-domain sheet music on IMSLP — the score is linked directly from this page.
Pieces at a comparable difficulty and character include Für Elise by Ludwig van Beethoven, Berceuse by Rudolf Friml, Albumblatt by Richard Wagner — see the full similar-pieces list on this page.