Yes, a contemporaneous, written record of your business miles is precisely the type of record that the IRS would like you to keep.

If you are taking the standard mileage rate, which for business miles  driven in 2016 was 54 cents per mile, you have no need for gas receipts. 

In completing the business mileage section of your tax return, you will be asked about three types of mileage: total miles driven for the year, business miles (which are deductible), and commuting miles (which are not deductible). It sounds like you may have an issue reconstructing your total miles for the year, since you did not keep records beyond your period of self-employment. My advice would be to use the best estimate you can obtain. If you have frequent oil changes, for example, the recorded mileage on the service orders closest to the beginning and end of the year may provide a reasonably close estimate of your total miles driven for the year.

For more information, please see IRS Tax Topics 510 Business Use of Car.