Whilst not being able to confirm James' father's name from the bible, what confirmation is there on father's occupation (you mentioned earlier he was possibly a Presbyterian minister & professor at the University of Edinburgh). Is this info also from the family bible or another source?
I assume that James's OPR marriage made no mention of father and with his early departure to Canada and young death, unlikely you will find verifiable sources there relating to his family. So, what info you have, such as potential occupation for James' father, may be key

You could try following through on some of the children showing for a James Paterson and C(K)atherine Bell, the parents of the James we found earlier. This is what shows on IGI:
1. ISABELLA PATERSON Birth: 12 MAY 1799/ Christening: 26 MAY 1799 Cadder Lanark
2. JOHN PATERSON Birth: 08 MAY 1801 Cadder, Lanark
3. WILLIAM PATERSON Birth: 23 APR 1803 Cadder, Lanark
4. JAMES PATTERSON Christening: 24 FEB 1805 New Kilpatrick, Dunbarton
5. REBECCA PATERSON Christening: 06 MAY 1807 New Kilpatrick, Dunbarton
6. JEAN PATERSON Christening: 22 MAY 1808 New Kilpatrick, Dunbarton
Only Isabella's christening entry shows as actual extract, the rest are all member submitted. I think some of these entries show on Scotlands People as actual extract, including a James. I searched mother's name as *ath* Bell to pick up on spelling variations. Also, it is a single 't' on Paterson on the search.
You may be lucky and find an occupation for the father William from the christening entries which would help.
Monica