A sinner's prayer is not necessarily wrong even though the prayer is not in the bible. I feel it is a good tool to lead those through the initial acknowledgement and confession of sins and accepting Jesus as their Lord and Savior. I also think the non-biblical opinion of asking Jesus into our heart is splitting hairs. You can ask him into your heart, body, soul, life, whatever; Jesus knows your heart and intent and He will squabble over proper working. JMO
As Romans states;
That if you confess with your mouth that "Jesus is Lord" and believe in your heart that God raised him from the dead, you will be saved.