John 6:44 suggests God's 'bid him to come' is more than an invitation that one is free to accept or decline. The fish that Peter 'bid to come ashore' in John 21:11 had no option to decline. When Paul was 'bid to come to the magistrate' in Acts 16:19 he was not free to accept or decline the invitation.
All three verses use the same word ... the Father DRAWS (John 6:44), Peter HAULS (John 21:11) and Paul was DRAGGED (Acts 16:19). When God 'bids come', we are more than 'free' to come ... we are drawn, hauled, dragged to the Son.
(All I can say for certain is that is how it was for me. I was not in any way, shape or form a 'seeker'. God ripped me from my old life by HIS choice, not by my choice. So where scripture and empirical experience confirm the same theological truth, that's where I am betting my money.)