Fox News said Bishop was handcuffed and taken by police to the county jail. She could be heard saying, "It didn't happen. There's no way ... they are still alive."
Apart from Bishop, police said they were interviewing a man as "a person of interest."
Bishop, a neurobiologist who studied at Harvard University, and her husband were placed third in a statewide university business plan competition in July 2007 for the portable cell incubator they had invented. They won USD 25,000
to help start a company to market the device.
The University of Alabama in Huntsville has about 7,500 students. It is known for its scientific and engineering programmes and often works closely with NASA.
Former Indian President A P J Abdul Kalam had visited the university last year.
In an editorial, 'The Huntsville Times' said the shooting "is sure to stir concerns among prospective students as they brace for a new university policy this fall that will require all freshmen and sophomores to live on campus."
The incident was the latest in a string of school shootings across the US, most of which have been carried out by students.
Last month, eight people were killed in a shooting incident in southern state of Virginia.
In April 2007, a student gunned down 32 people at the Virginia Tech university, before turning the weapon on himself.