What the company pays will affect what you pay. That said, rates can vary depending on the price that they pay, as well as other factors that are used within the business. For example, one energy provider could offer lower prices simply because they are able to run their business in a less expensive manner. Prices can be cut without any relation to fossil fuels.
Be careful not to confuse lower prices with a lower level of service. There are companies that are willing to accept a lower profit margin in order to secure more business. The level of service that is provided can remain as high, or even exceed that of other companies.
Fossil fuels are indeed a part of what makes up your business gas bill each month. However, they are not the only factor. It will be important to consider your energy provider options, as not all companies offer the same level of pricing. Lower prices could very well be in your future.