Resuming at the overnight score of 118 for five after bowling out Sri Lanka A for a measly 145, the visitors struggled to get going against the leg-spin of Bandara folding up for 157.
Bandara finished with figures of 8-49.
The hosts wiped off the two run first lead to dash out in front by 199 runs, reaching 211-5 at stumps on the second day.
Shantha Kalavitigoda hit a patient 83 as the tourists experimented with eight bowlers. For England, Ian Bell snapped up two wickets.