No--do not pay your personal bills out of the business account. Hopefully you have created a business plan. You need to assess what the business can afford to pay you and you should visit with your personal accountant regarding this as well. Normally we will take a portion of our payment as payroll expense and the other as an equity withdrawal - they are taxed differently. Then from this payment you will pay your personal bills out of your personal account. Do not comingle funds - keep business and personal separate.
If you're an entrepreneur, it's critical to find a tax preparer who understands the tax implications of owning a small business as well as your particular needs in order to establish a beneficial relationship.