As far as I can tell, there is currently no way to modify a custom monster's initiative bonus past adjusting their dexterity scores. This is rather annoying, as I would like to add bonuses that would be similar to having the Alert feat, without having to write down the fact that a monster has a bonus to initiative somewhere in the special features section. I like to make monster sheets that are as streamlined as possible, so having a way to adjust initiative so that it just gives you a bonus on the "roll initiative!" prompt would be greatly appreciated.

Monsters do not list their initiative on their stat block, so you would have to put this information in their traits. 

You can add a custom Initiative bonus by adding a custom rollable into a special trait, I do it for monsters all the time.

Leap Into Action. This monster has an additional [_rollable]+3;{"diceNotation":"1d20+7","rollType":"roll","rollAction":"Initiative"}[/rollable_] bonus to its initiative rolls.

Note: The special trait lists a +3 bonus (the monster’s PB) but the actual rollable is set to +7 to account for the monster’s Dexterity bonus as well. You can adjust those numbers to suit your needs.

Thanks for the coding to this. I'll make sure to save this for future monsters.

Happy to help?

Edit: Sometimes I code it like this instead (I can’t decide which I prefer):

Leap Into Action. This monster has an additional +3 bonus to its [_rollable]initiative;{"diceNotation":"1d20+7","rollType":"roll","rollAction":"Initiative"}[/rollable_] rolls.