Okay, so I worked it out.
first, take each item you are combining and figure out the total pure ethanol in each.
(Beer Volume (gallons) X ABV beer (as a decimal))
+ (Bourbon Volume (gallons) X ABV bourbon (as a decimal))
Then you divide by the total volume of both items combined.
/(Beer Volume + Bourbon Volume) that will tell your your new ABV.
Algebra.
(V1*A1+V2*A2)/(V1+V2)=A3
Where V is the volume (liters or gallons: doesn't matter just use the same unit for both volumes considered), and A is the alcohol content.
To reverse it and reach a specified ABV by adding a quantity of bourbon,
(V1*(A1-A3))/(A3-A2)=V2, where V2 is the quantity of bourbon you need to add to achieve an alcohol percentage of A3.
V1 and A1 are your beer (volume and alcohol decimal), V2 and A2 are your bourbon (volume and alcohol decimal), and A3 is the final Alcohol of the combined product.