A Texas member of Congress, concerned that a homemade bomb slipped past National Airport security in the baggage of a Dallas-bound commercial airplane, called yesterday for a full-scale investigation of bomb-detection procedures by the Federal Aviation Administration.

Democratic Rep. Martin Frost, in a letter to FAA Administrator J. Lynn Helms, said that the nation's passenger flights may have "a severe security problem." His comments were provoked by the arrest of an Andrews Air Force Base mechanic who was charged with attempting to destroy a commercial airplane by hiding a bomb in his wife's suitcase.

According to FBI agents, Airman 1st Class Martin Thomas Bradley, 27, placed a plastic explosive device in his wife's suitcase before it was checked in the hold of Braniff Flight 111 last Tuesday morning. The bomb was not discovered until Staff Sgt. Mary Jo Bradley arrived at Sheppard Air Force Base in Wichita Falls, Tex.

"The fact that I and many other members of Congress from Texas use that particular flight brings the impact that much closer to home," Frost said in the letter. An aide to Frost noted that Rep. J.J. Pickle (D-Tex.) was on the same Braniff flight one day before the bomb incident.