How do I calculate Base64 conversion rate?
However, I do not know what length I need to have the signature at so when I encode it, it can be that exact size.

Well, base64 uses 4 characters (from an alphabet of size 64) to encode 3 bytes (3 bits contain 24 bits; 24/4 = 6 bits per base64 character).
Hence, if the signature was 72 bytes long, that would translate to 72/3*4 = 96 characters you require.
Now, base64 typically has a === trailer to signify the end of the encoding; are you counting that?