A SMALL HIGH WING ACFT ON LNDG ROLLOUT AT A HIGH RATE OF SPD TURNED OFF THE RWY ONTO A TXWY AND INCURRED A TXWY EXCURSION.

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MY GIRLFRIEND IS TAKING LESSONS FOR HER PLT'S CERTIFICATE. SHE AND I WERE TO FLY THE NEXT DAY TOGETHER. I ASKED MY CFI IF THERE WAS ANY RULE AGAINST ME FLYING IN THE R SEAT AND SHE IN THE L. HE SAID HE DIDN'T THINK THERE WAS ANY SPECIFIC RULE AGAINST FLYING IN THE R SEAT. HE DID RECOMMEND THAT I TAKE A PRACTICE FLT IN THE R SEAT BEFORE I WENT UP WITH HER JUST TO MAKE SURE I DIDN'T HAVE A PROB WITH MY ORIENTATION IN THE R SEAT. I FLEW TO FRONT RANGE ARPT IN THE L SEAT; LANDED; PUT GAS IN THE PLANE; AND THEN TOOK OFF IN THE R SEAT. I FLEW AROUND IN A PRACTICE AREA FOR A WHILE GETTING FAMILIAR WITH FLYING IN THE R SEAT. IT WAS DIFFICULT TO SEE THE TURN COORDINATOR AND THE AIRSPD INDICATOR FROM THE R SEAT. I THEN ENTERED THE PATTERN TO LAND AT FRONT RANGE ON RWY 8. WINDS WERE 050 DEGS AT 11 KTS. SITTING IN THE R SEAT FELT STRANGE. I DIDN'T HAVE ANY PROB ON THE APCH. HOWEVER; AFTER I SET THE WHEELS DOWN ON THE RWY; I COULD NOT KEEP THE PLANE FROM DRIFTING TO THE R. I TURNED ONTO THE R TXWY (APPROX TXWY A6) AT A HIGH RATE OF SPD AND WAS UNABLE TO KEEP THE PLANE ON THE TXWY. THE PLANE WENT INTO THE GRASS ALONG THE TXWY AND CAME TO A STOP ON TXWY A AFTER GOING THROUGH THE GRASS. THERE WAS NO DAMAGE TO PLANE.