Maybe not. GHWB was never a senator, but he did serve I the House.
The 1970 United States Senate election in Texas was held on November 3, 1970. Incumbent Democratic U.S. Senator Ralph Yarborough was defeated by former Representative Lloyd Bentsen in the Democratic primary. Bentsen then defeated Representative George H.W. Bush in the general election.
https://ballotpedia.org/George_H.W._Bush
more from that site:
He began his career in politics in 1963, when he became the chair of the Republican Party of Harris County.[2] He ran for a seat in the U.S. Senate in 1964 but was defeated by Democratic incumbent Ralph Yarborough. Bush won election to the U.S. House seat representing the 7th District of Texas in 1966 and 1968.He tried again for the same Senate seat in 1970, but was defeated by Democrat Lloyd Bentsen.[4]