Ireland is a significant factor in the history of the Bells as many families may have came to Ulster during the Plantation in the early part of the 1600s before emigrating to other parts of the World due to vast and various reasons.
As forwarded to the Collins Scottish Clan and Family Encyclopaedia by the Rt. Hon. ME Earl of Eglin KT. Covenor of the Standing Council of Scottish Chiefs, the Bells were believed to have been descendants of a Norman follower of David 1st who reigned until 1153 AD.
There is also the Macmillan claim that the name Bell is derived from their own. It is stated in the Macmillan clan history in the Collins Scottish Clan and Family Encyclopaedia that when David 1st abolished mormaership of Moray the Macmillans moved to the Loch Archaig area where they settled along with Norman Knights.
It could be Possible that some of the Norman Knights who settled along with the Macmillan's could have already held the name Bell or more likely 'bel'. The History books show us that on various occasions the Norman's integrated themselves into their new surroundings, examples can be shown in Ireland, England, Scotland and of course their launch pad of Normandy in the North of France.