Two masked men armed with kitchen knives fled with "a few hundred pounds" after threatening staff at Betfred in Old Christchurch Road on Thursday.
It follows raids at Ladbrokes in Seabourne Road on Wednesday and at a Londis store in Boscombe on Monday.
On both of those occasions the masked offender used a baseball bat.
In the Ladbrokes store, the man stole cash from the tills before making off on foot.
At the Londis store, the raider smashed a National Lottery box and fled with scratch cards.
A police spokeswoman said: "At this stage we cannot conclude they are linked but we are keeping an open mind and are investigating all three."
Armed raiders have struck a third time in the space of three days in Bournemouth, with police keeping an "open mind" on whether they are linked.