I use 4.1 grains of Bullseye with 115 grain Copper jacketed bullets (like Rainier or Berry's).
The Alliant or Speer numbers are the maximum loads for FMJ bullets. You don't want to load maximum. Keep it a bit below to ensure that if you get variation of 0.1 to 0.2 gr throughout the lot, or other variations in brass or whatever, you will still be safe. You may also be a bit more accurate when loading below maximum.
Lyman says 4.8gr is the max Bullseye load for 115gr Metal Jacketed bullets
Lee says 5.0gr is the max Bullseye load for 115gr Metal Jacketed bullets.
If I want a more powerful round I don't up the bullseye powder charge. I instead use a different powder. 6.0gr of Alliant Power Pistol with 115gr copper bullet gives a nice deep bang. My favorite 9mm load.