Reinsert data in new table with new IDs
I guess you can do the following:
1. In your new table buynsell, add a column , old_id
2. Reinsert data from the old table as you said, skipping auto_increment field, and storing old_buynsell.id as old_id in your new table.
3. Import data to new replies table
4. Update bns_id column in replies :

UPDATE replies a
INNER JOIN (select id, old_id FROM buynsell) b ON (b.old_id = a.bns_id)
SET a.bns_id=b.id


5 Drop old_id column, you don't need it anymore.