I think another factor in the relative silence about Bauman is that he set his record toward the end of an era in which there was often a huge discrepancy in talent levels among minor leaguers at a particular level. While the farm-team system was well-established by this time, there were still leagues where almost none of the clubs had working agreements with major league clubs.
Such was the case with the Longhorn League in 1954; only one of the eight clubs in the league had a working agreement with a big league team, and it wasn’t Bauman’s Roswell Rockets (if you must know, it was the Wichita Falls/Sweetwater Spudders, who were a Washington farm club). Management of such teams scrambled to find players wherever they could, and if they came across a guy like Bauman (who bought his own release from Artesia in the same league a couple of years before to sign with Roswell) who was quite capable of playing at a higher classification but who wanted to settle down locally and play for the hometown nine, so much the better – neither the club nor the player worried about what it might do to the level of competition.
Bauman himself supposedly turned down lots of offers to play at higher levels both before and after 1954 (he’d played in the American Association and Eastern League briefly before his stint in the Longhorn League). He was content to run his gas station and other local business interests in Roswell, whallop the hell out of Class C pitching (which certainly didn’t hurt business at the gas station), and make a lot more money with a lot more security than he’d have had knocking around from city to city, league to league for another five or six years. With only eight teams in each league at the major league level, a whole lot of talented players decided that the security and local celebrity that came from settling down and playing for the local team for several years meant more money and a lot saner life than trying to crack the show. Bauman’s is only one of the best-known cases.
Within a few years, however, such a career was no longer an option. By 1960, nearly every remaining minor league team (dozens folded in the mid/late 1950s) was affiliated with a big league club. Take Bauman’s Longhorn League: it grew to ten clubs in 1956, of which two had working agreements, shrank back to eight in 1957, again with two farm teams, then down to six in 1958, with all of them being farm clubs of major league teams. That remained the case until the league folded in 1961.
Even after the demise of independent minor league teams in the late 1950s, there were still a few guys who kicked around signing independent deals directly with the minor league club rather than the parent team, but they’ve grown rarer as the years have gone by, until today the practice is pretty much unheard-of. The rise of independent minor leagues has given such players a place to play, and the big league clubs don’t like ringers messing with the level of play in organized ball.
So you have to take Bauman’s accomplishment (and accomplishment it was) in that context. It’d be like Rob Deer or Pete Incaviglia electing to play at today’s Class A level, say in the South Atlantic League at Spartanburg in that old bandbox Duncan Park (dimensions: LF=319, CF=376, RF=319, compared with something like 330-385-330 in the thin air at Roswell), instead of kicking back and forth between AAA and the majors for years.