The One Tree Hill star announced his engagement to Kenzie Dalton, a high school student, last week.
Bush filed for an annulment in February, on grounds of fraud and their divorce has not been finalized.
When asked by People magazine if the rumors of pregnancy were true, Murray said, "Definitely not."
Dalton's mother, Jeannie, confirms the couple are "crazy for one another."
The pair have not made any final wedding plans, but Murray says he is determined to have a long-lasting relationship this time around.
He adds, "(All I want is) to be 80-years-old and to have been married for 50 years and still be so in love."
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