Having posted 316 on Friday, Joe Root's side took to the field and removed both openers as an SLC Board XI reached 83 for three at lunch.
Stuart Broad shared the new ball with left-armer Sam Curran, but it was Woakes who got the tourists going after replacing the latter.
Woakes, who this week informed Delhi Capitals of his withdrawal from the Indian Premier League to focus on his international duties, produced a couple of lively short balls before Lahiru Udara took on the pull and top-edged to Broad at mid-on. The Warwickshire man would have added a second but Root put down a chance at slip.
Bess had been introduced early in the piece, taking the seventh over, and after one strong lbw appeal was rejected he dismissed Sangeeth Cooray with a sharp caught and bowled.
With match conditions allowing all squad members to take part, England used six bowlers, including spells from uncapped Lancashire duo Parkinson and Saqib Mahmood.
Mahmood bowled four eye-catching overs for six runs, but it was Parkinson's leg-spin that ensured a breakthrough just before lunch, Lahiru Milantha chipping to extra cover.