The Right Reverend Graham Tomlin said residents should be at the heart of the investigation, which is believed to have killed at least 80 people.
"If you keep... the people directly affected by it out of the inquiry process, it just takes an awful lot longer to get to the truth," he said.
Dr Tomlin, whose diocese includes the tower, said local trust was important.
His remarks were mirrored in his formal submission to the public consultation, which closed on Friday.
It is believed more than 300 submissions were made before the deadline.
Inquiry chairman Sir Martin Moore-Bick, a retired Court of Appeal judge, has already faced calls to resign from some residents of the west London tower block.
"It seems to me that the inquiry needs to get to the truth... but it also needs to win the confidence of the local people," Dr Tomlin told the BBC.
If it does not, he said, "whatever recommendations it makes is unlikely to get support."
He said the inquiry needs to not only look at the technical causes of the fire on the night in question, but also the issues faced by the community in the run-up to the tragedy.
"I want to see local people at the heart of the inquiry, not just on the outside," he said.
Residents' group Justice 4 Grenfell also made several submissions to the consultation process, including calling for investigation of the local council and a number of  government departments.
The fire in the 24-storey block started in a fridge freezer and destroyed 151 homes, both in the tower and surrounding areas.
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The Scottish government is to change the law to make sure children spend a minimum of 25 hours a week in class.
It follows rows over attempts by some councils to reduce the length of the school week to help balance their books.
Nobody in the mainstream has seriously argued that a cut in the school week would actually help improve children's attainment.
Councils which have looked at the idea would argue they have done so out of financial necessity. Their argument has, essentially, been that a cut in the school week for some is a "least worst option".
When West Dunbartonshire advanced the idea earlier this year, they argued that the cut would affect things such as assemblies and "golden time" - not actual teaching time in the classroom.
The savings come, for instance, by reducing the number of hours when the building itself is open.
Parents have often reacted angrily to the proposals though. Quite apart from any concern they may have about their children's education suffering, some would face practical problems with childcare.
With local government funding tight, the problem comes with the amount of flexibility councils have to find the best ways to balance their books.
Education in Scotland is, essentially, a national service which councils are entrusted to deliver.
There are many nationally set rules and guidelines. For instance, teachers' pay and conditions are standardised across Scotland and there are already minimum requirements on the number of days when schools have to be opened.
Councils get the bulk of their money from the Scottish government and the latest funding deal commits councils to maintaining the number of teachers - even though some had argued that was not necessarily the best use of their resources.
Councils are under a legal obligation to balance their books. If one potential option for savings is closed, inevitably, it could lead to greater pressure on another service.
Local government organisation Cosla is also angry about the government's announcement, claiming there had been a lack of consultation.
Some in local government argue councils need greater financial freedom to be able to properly respond to local needs.
They see the current financial settlement as something of a straightjacket because they have little real control over the overall size of their budget.
A report in the next few weeks by a commission set up by the Scottish government and Cosla will outline various alternatives to the council tax - the tax which typically raises around 15p of every pound councils spend.
In some council chambers, there will be disappointment if the debate is not widened to also look at whether councils should be less dependent on central government for cash and have more options on how to raise money locally.
The Bishop of Kensington has called for locals to be closely involved in the Grenfell Tower fire inquiry.
[NEXT_CONCEPT]
The reaction by some in local government to moves to stop the length of the primary school week being cut is, ultimately, more about money than education.