The phrase “like a bump on a log” means: Like a Stoughton bottle; stolid; unemotional; stupidly dumb.
Usually any such dumb bunny is said to sit or stand like a bump on a log, meaning just to sit or stand in vacuous silence.
The metaphor is American and may have referred originally to the stolid protuberance found on almost any log, or it may have been suggested as a comparison of the discomfort from sitting on a bumpy log with the discomfort of association with a superbly dumb companion.
Undoubtedly the description was used long before her time, but it seems to have appeared first in Kate Douglas Wiggins’ The Bird’s Christmas Carol (1899): “Ye ain’t goin’ to set there like a bump on a log ‘thout sayin’ a word to pay for yer vittles, air ye?”