Shorey's 101 and Bhui's 91 enabled Board President XI to declare their first innings at 397 for 6 in 108 overs, at tea on the final day.
Post tea, South Africa 'A' reached 62 for 2 before the umpires decided to call off the match before the start of mandatory overs.
Starting the day at 201 for 2, Shorey, who scored a hundred during last edition's Ranji Trophy final, duly completed his century. His innings was laced with 16 fours and a six. The Shorey-Bhui combination added 94 runs for the third wicket.
Shorey, however, will not add to his list of first-class hundreds as this match was not accorded that status.
Shorey edged one to keeper Rudi Second off seamer Mthiwekhaya Nabe as Bhui looked in good touch. He hit 13 boundaries and a six before being adjudged leg before off leg break bowler Shaun von Borg.
Mumbai's Siddhesh Lad (10) and Punjab's Anmolpreet Singh (32) missed out on a big score on a placid track while Ishan Kishan remained unbeaten on 17. Von Borg was the most successful Proteas bowler with figures of 3 for 62 in 17 overs.
In the inconsequential second innings of South Africa, leg-spinner Mihir Hirwani got a couple of wickets.
South Africa A 1st Innings 473 for 4 decl & 62/2 (Mihir Hirwani 2/35).
Board President XI 397/6 decl in 108 overs (Dhruv Shorey 101, Ricky Bhui 91, Sanjay Ramaswamy 87). Result: Match drawn.
First Published: August 1, 2018, 6:25 PM IST