I have added in the following points raised at the Haringey Cycling Conference 24/09/15.
Office costs reduced
Varied services may be available, ie beyond Bikeability
Experience of work in other boroughs/counties
Stuck with provider/need to manage relationship
There may be a pre-procured solution, eg in London TfL have a Pan London contract with a provider that borough can access.
You might be able to get funding from the YST.
Do a site visit and see your prospective provider's training in action.
Read the TABS Procurement Guidance.