Can certain users on my B2B site be required to use a budget but other users do not need to use a budget?

Budgets are a site wide setting - not user-specific; however, you may adjust the Site Group permissions to enable customers within that group to be able to checkout without a budget.

Once Budgets are enabled on a site, by default all site users must select a budget at check out. You may override this requirement by adding users to a Site Group that has the permission "Can checkout without selecting a budget."