Bavuma came to the crease with the Lions battling on 70 for three, and saw Alviro Petersen depart soon afterwards to leave them 86 for four.
With Sunfoil Series debutant Nicky van den Bergh and then Dwaine Pretorius providing some stability at the other end, Bavuma led a slow and steady recovery that took the Lions to 169 for five before bad light stopped play with just 69 overs bowled on the day.
Bavuma finished unbeaten on 52 not out, giving him the opportunity to extend his preparations for the Proteas’ four-Test series against England under pressure conditions when play resumes on Friday.
He will have Pretorius for company after the all-rounder added an unbroken 42 with Bavuma to close the day on 21 not out.
The chief trouble-maker for the Dolphins was seamer Calvin Savage, who had Dominic Hendricks and Petersen caught behind and then returned to trap Van den Bergh lbw shortly before the tea break.
The 22-year-old finished the day with figures of 3 for 49 in 20 overs, seven of which were maidens.
That reflected the consistency with which the Dolphins bowled throughout the day, limiting the Lions to a run rate of well under three per over.