While the name Bolle is seen most commonly in the Canterbury references and Bole is seen most commonly in Ickham references, the distinction is likely insignificant.  Please see the discussion of this question in Middle English Origins of the Boles Name

The Kent Hundred Rolls of 1274-75 listing for The Hundred 0f Westgate includes a Henry Bolle.  The Hundred of Westgate was the area just outside the West gate of Canterbury. 

At a Consanguinity Hearing at Christ Church, Canterbury in 1294, depositions were made by William and Eylmer Bolle.  ref. 

The Roll of Freemen of Canterbury for 1356/57 includes only 17 names including Thomas Bolle, cooper. ref.  The Roll of Freemen of the City of Canterbury from 1392 to 1800 includes: by birth,  John, son of Thomas Bolle, cooper (in 1400); by marriage, Henry Bolde, clerk, married to Isabella, daughter of John Lynde (1400); John Bowles, smith, married to Elizabeth, daughter of Anthony Brown, baker (1747);  Laurence Bowles of Birchington, gent. (1760); Robert Shorte married to Joan daughter of William Boole (1483) and by Redemption, Anthony Bowles, victualler (1749).

In 1395 a Thomas Bolle witnessed a land grant signed in Canterbury between William atte Berton of Ickham and John Skyrmour of Canterbury involving land next to Bertonesfeld in St. Paul's parish outside the gate leading to the eastern suburbs of Canterbury. ref.

Although the Canterbury Cathedral Archives online catalogue is very extensive, there are no further references for Bolles in the immediate neighbourhood of Canterbury.  However, the first Bolles references at Chartham just a couple of miles SW of Canterbury commence in 1407 and feature the given names William and Thomas.  See The Bolles of Chartham for the probable continuation of this line.

The Calendar of Wills and Administrations lists a Will for only one Bolle of Canterbury, John Bolle in 1484 and for one east of Canterbury, William Bolle of Patrixbourne (1531).