You say that your "router" is rented from your "link provider", and they don't give you access to it. Does that mean that you have no border or core devices that you control? If so, I'd say you're screwed (and seriously abrogating your responsibilities as a provider of network services).
Assuming you have got something in place that you control, you can monitor in any number of ways.
At the IP level, you'll either want something that exports netflow data from your border to an analysis station. Since you don't give any useful information as to what your environment consists of, there's no specific recommendations I can give, but Google "
<your platform> netflow" to get useful results.
At the port level, SNMP statistics should be sufficient to give you billable bandwidth numbers. Again, without knowing your platform, it's impossible to know which SNMP manager to recommend.