PIPER PA38 STUDENT AND INSTRUCTOR HAVE AN NMAC DURING DEP FROM GTU.

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MY STUDENT TOOK OFF ON RWY 18 AT GTU ARPT AND AT 500 FT AGL STARTED A TURN TO THE SE IN ORDER TO FLY TO OUR FLT SCHOOL'S PRACTICE AREA TO THE E OF THE ARPT. DURING OUR CLBOUT; I HEARD A BONANZA ANNOUNCE THAT HE WAS 5 MI TO THE SE; INBOUND ON THE 45 DEG ENTRY FOR THE L DOWNWIND FOR RWY 18 AT GEORGETOWN. I MENTALLY NOTED THAT THIS ACFT COULD POSE A POTENTIAL COLLISION HAZARD. MY STUDENT'S HDG WAS DRIFTING L OFF COURSE TO 110-120 DEGS INSTEAD OF THE 140 DEGS I WANTED FOR HIM TO FLY; I ALSO MENTIONED THAT WE HAD A BONANZA INBOUND ON THE 45 DEG. AT THIS TIME WE WERE AT ABOUT 1200 FT AGL AND DEPARTING THE PATTERN. NO SOONER THAN I MENTIONED THIS THAN I OBSERVED THE BONANZA ABOUT 1 MI DIRECTLY IN FRONT OF US ON A DIRECT COLLISION COURSE. I POINTED THE TFC OUT TO MY STUDENT WHO HESITATED; I IMMEDIATELY TOLD HIM TO TURN TO THE R TO AVOID THE TFC; WHICH HE THEN DID. ABOUT 2 SECONDS LATER THE BONANZA MUST HAVE ALSO OBSERVED US AND STARTED A TURN TO HIS R. THE BONANZA PASSED OFF OUR L WING; AT OUR ALT AND ABOUT 300 FT AWAY. WE CONTINUED OUR CLB TO 1500 FT AGL BEFORE TURNING ON COURSE.