What looks like your bottle is illustrated in Bitters Bottles, by Richard
Watson, Thos. Nelson and Sons, New York, 1965, page 70.   He does not date
it, but offers the following comment:

"The label is identical to that for Greeley's Bourbon Bitters.  Marked
"Pollard and Co., Boston, Mass."  Refer to Greeley's Bourbon Bitters for
further discussion."

Under Greeley's on page 116,  refers to confusion between Pollard, Greeley's,
and yours.    So there are several avenues to pursue the research.  Hope this
helps.

Roberta Greenwood