Bodacious is commonly defined as meaning variously blatant, audacious, impressive, remarkable or attractive. As you can tell from its wide-spectrum definition, this American word is one of those wide-ranging superlatives to which speakers turn when they want to say that some quality is present in large degree; that quality might be unreasonableness, impressiveness, insolence, or (most recently) female attraction, specifically big breasts. This last meaning seems to have become widely known in the middle 1980s after it was employed in the film An Officer and a Gentleman in 1982. Another film, Bill and Ted’s Excellent Adventure of 1989, contributed to its growing nationwide popularity.
As a result, many people would guess the word is modern, but the earliest record (actually of the adverb bodaciously, which appeared as body-aciously) is from as long ago as 1832. The adjective is known from the 1840s, often as bowdacious in the early years. This leads lexicographers to think that both it and the adverb are from an English West Country dialect form, written as boldacious or bowldacious, which was probably an amalgam of bold and audacious.
Among older users and before its recent surge to popularity, the word seems to have been most common in the American South, though not among African-Americans. One of the earliest examples is from Georgia, dated 1845: “She’s so bowdacious unreasonable when she’s riled”.