Jim McGrath, the family's spokesman, said that 41 will continue his recovery and regain his strength through the weekend.
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On Wednesday, Jim McGrath said Bush is "alert and talking with hospital staff, family and friends, and his doctors are very pleased with his progress."
In a tweet, Bush also thanked everyone who helped with the public visitation and private funeral for the former first lady.
He wrote, "My family and I thank Mayor Sylvester Turner, his terrific staff, Houston Police, METRO Houston, Second Baptist Church, St. Martins -- and really all Houstonians -- for your professionalism and obvious care in making Barbara's visitors and funeral guests feel so welcomed. Thank you all."