He offered to answer emails on inspections and his annual report as part of a drive to make Ofsted a more "listening" organisation.
Several teachers emailed saying they were confused by a comment in his report last week that satisfactory teaching was no longer good enough.
Timothy Rose, head of St Mary's Church of England primary in Sheffield, wrote: "A dictionary definition of satisfactory is 'sufficent to meet a demand or requirement' or 'adequate'.
"If, as a profession, what is regarded as satisfactory is not sufficient, there needs to be a fundamental change in definitions."
Mr Bell replied: "I know that satisfactory is, in one sense, that which satisfies. But in much of what we do, we seek more than just satisfaction.
And so it should be in education."
He was less impressed by the question from an anonymous teacher, who asked what should be done about those who are "only satisfactory and really can't be bothered to get any better".
"I hope you are being facetious," Mr Bell replied. "None of us is perfect, but I hope that we all strive to do better particularly when the education of children is at stake."
Asked whether he felt paying teachers more would improve recruitment and retention Mr Bell was diplomatic, admitting pay had "something to do it" but saying problems like pupil behaviour could make the job unsatisfying.
Several teachers agreed with the chief inspector that virtually all schools suffered from a group of anti-social pupils.
Others suggested changes to the inspection system. Hugh Robinson, head of Minster College in Kent, urged Ofsted to release reports only to schools, governors, and LEAs, instead of publishing them.
"Could we tackle the problems together without demotivating our profession or spooking our customers?" he asked.
But Mr Bell said it remained essential for Ofsted to inform parents and communities about school standards. The inspector's annual report, published last week, warned that refugee and asylum-seekers could be a considerable drain on schools' resources, and disrupt teaching and learning.
Janet Price is head of Southfields primary in Coventry, where 36 per cent of pupils are asylum-seekers. "Working with asylum-seekerpupils is a considerable challenge, but it is also a great privilege," she wrote. Mr Bell has asked to visit Southfields to see for himself.
Full letters and replies at www.tes.co.uk