Image DPI

There are two things here.

First, the PPI that your printer has requested. That is easy - you use Image Size - with resample to give that resolution. That way you can send the printer the file he has requested.

The second, which does not affect any vector parts of the image (i.e. text or shapes) but does affect the pixel image,  is how many pixels does your image need to be acceptable for viewing. Unless your billboard will be viewed from a few cm away with a magnifying glass then you don't need to start with 300ppi. The ppi needed depends on viewing distance. Our eyes can only resolve so much detail.
As a rule of thumb - the viewing distance is about 1.5 x the diagonal so in your case - about 10-12 metres (approx. 480 inches)

There is a formula in the link below for working out the ppi required at a given viewing distance. In your case it suggests around 15 ppi.  So your 12 metre length needs to be around 7000 pixels - anything else is a waste, because you won't see it at the normal viewing distance.

What print resolution works for what viewing distance?

In short get your image looking good at 100% zoom and 7000 x  1750 pixels. Then do a final increase in size to the dimensions required by your printer.

Dave