PA32 PLT HAS NMAC DEPARTING BMT.

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I ADVISED I WOULD BE TAKING OFF FROM RWY 31L AND WAS TOLD TO 'HOLD FOR RELEASE.' I DID SO. I WAS TOLD BY CLRNC DELIVERY OF RELEASE INTO CTLED AIRSPACE AND TO 'ENTER CTLED AIRSPACE HDG 300 DEGS.' DURING ALL TIMES; I MONITORED THE UNICOM FREQ ON THE SECOND RADIO. I CHKED THE AREA AND ADVISED TFC ON 123.0 THAT I WAS 'TAKING OFF RWY 31; DEPARTING TO THE NW.' THERE WAS NO REPLY. I DID SEE A LOW WING PIPER ACFT ON DOWNWIND LEG TO RWY 31; BUT IT APPEARED TO BE BREAKING OUT OF THE TFC PATTERN ON A 45 DEG LEG TO THE SW. AFTER TKOF; I ALTERED COURSE SLIGHTLY TO THE L TO A HDG OF 300 DEGS. AT THAT MOMENT; THE LOW WINGED PIPER SUDDENLY APPEARED FROM MY L; SLIGHTLY BUT HEAD-ON TO ME. I PASSED DIRECTLY UNDER THE OTHER PLANE. THERE WAS NO TIME TO REACT. THE CONVERGING AIRPLANE HAD BEEN OBSCURED BY MY L WINDSHIELD POST. THIS WAS THE SAME PLANE THAT HAD BEEN DOWNWIND TO RWY 31. IT HAD REVERSED ITS DIRECTION AND HAD ENTERED A BASE OR FINAL LEG TO RWY 13. I NEVER HEARD ANY POS RPTS FROM THIS OTHER AIRPLANE. UPON RETURNING TO THE ARPT LATER THAT DAY; WITNESSES CONFIRMED THAT THE OTHER AIRPLANE DID NOT AT ANY TIME CONTACT UNICOM FOR TA'S AND HAD NOT BROADCAST ANY POS RPTS. WITNESSES SAID THE OTHER PLANE MADE A VERY POOR 'BOUNCING AND PORPOISING LNDG' ON RWY 31 AFTER 1 GAR MANEUVER ON RWY 13. THE OTHER AIRPLANE WAS NOT BASED AT ARPT; RPTEDLY WAS BASED IN ANOTHER AREA. WITNESSES WHO ATTEMPTED TO COUNSEL THE PLT OF THE OTHER PLANE RPT THAT HE WAS UNDER THE IMPRESSION THAT RWY 13 WAS ACTIVE BECAUSE THAT WAS THE 'CALM WIND' RWY. HE ALSO TOLD THE WITNESSES HE WAS MONITORING UNICOM FREQ 'BUT NEVER HEARD ANYTHING' AS IF HIS RADIO VOLUME CTL WAS TURNED DOWN. IT WAS THE IMPRESSION OF THE WITNESSES THAT PLT OF THE OTHER AIRPLANE NEVER AT ANY TIME SAW MY AIRPLANE; OR THE ONE BEHIND ME IN LINE FOR TKOF; AND DID NOT REALIZE HE HAD AN NMAC EXPERIENCE.