Gta 5- Director mode

To answer the question, no. There is no way. The best way would be to just press X (A on XBox) when the game starts loading. If you accidentally load into story mode, you can use the Switcher and choose the bottom character to switch to your online character instead of having to go through the menu.

You should be able to change your character in online mode to one of the 3 from story. After this, your game will switch to story mode. You should be able to play in story mode for as long as you want.

Also, when the game start to load online mode, you should be able to switch with a button (I don't remember which one but it should be shown on loading screen).