WHILE PRACTICING LNDGS; PVT PLT OF A C305; BIRD DOG; LOST DIRECTIONAL CTL OF THE ACFT DURING LNDG ROLL RESULTING IN RUNNING OFF THE SIDE OF THE RWY.

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IT HAD BEEN 2 MONTHS SINCE LAST FLYING THE TAIL DRAGGER L19A CESSNA. I HAD BEEN FLYING A PA24 REGULARLY AND HAD JUST FINISHED A 2.3 HR TRIP FROM 68J (TALLAHASSEE COMMERCIAL) TO EQY. THE WX WAS BEAUTIFUL AND THE WINDS WERE LIGHT AND VARIABLE TO 6 KTS FROM 060 DEGS. AS THE RWY IS RWY 5 AT MONROE; I DECIDED TO FLY THE L-19A. AFTER PREFLT AND WARM-UP; I TOOK OFF TO STAY IN THE PATTERN TO DO SOME TKOFS AND LNDGS. I HAD A GOOD FINAL APCH ON THE FIRST LNDG; SET THE ACFT DOWN; HAD A SLIGHT BOUNCE WHILE EXECUTING A 3 POINT LNDG. ADDED SLIGHT PWR TO ARREST THE BOUNCE SET THE PLANE BACK DOWN. IT WAS STRAIGHT. NO WIND TO SEE ON THE WINDSOCK. THE STICK WAS BACK AND THE PLANE WAS ROLLING OUT NORMAL AND STRAIGHT WHEN I APPLIED THE BRAKES. THE NEXT INSTANT I WAS HEADED TO THE L WITH THE R WING DOWN. THE R TIRE LEAVING BLACK MARKS ON THE RWY AND DESPITE LETTING OFF THE BRAKES AND APPLYING RUDDER TO STRAIGHTEN THE ACFT. THE PLANE CONTINUED TO THE L IN A CURVING PATH AND RAN OFF THE RWY INTO THE GRASS WHERE IT STOPPED FACING BACK TOWARDS THE APCH END OF THE RWY. I CHKED THE GND LIGHTS; NO HITS ON ANYTHING. THE ENG WAS RUNNING CORRECTLY; THE WINGS HAD NOT CONTACTED THE GND. I THEN TAXIED BACK TO AN APRON AREA NEAR THE PLANE'S NORMAL TIE-DOWN SPOT VIA THE TXWY. I SHUT DOWN THE ACFT AND INSPECTED THE TIRES; BRAKES; PROP; WINGTIPS; NAV LIGHTS; RUDDER AREA AND TAILWHEEL AREA. I CHKED THE CTL OP. ALL ITEMS WERE FINE. I THEN STARTED THE PLANE; TAXIED OUT AND DID A COMPLETE RUN-UP. I TOOK OFF AND MADE 2 MORE UNEVENTFUL NORMAL 3 POINT LNDGS TO FULL STOP. I THEN TAXIED BACK AND TIED DOWN THE ACFT. I CAN ONLY FIGURE THAT I APPLIED DIFFERENTIAL BRAKING THAT STARTED THE LOW SPD SWING TO THE L THAT I WAS NOT SUBSEQUENTLY ABLE TO CTL. THE LACK OF CONSISTENT PRACTICE DEFINITELY CONTRIBUTED TO THIS SIT.