I wouldn't worry about tailoring fertilizer to bulb vs plants. Skip the bulb food since you are fertilizing for perennials.
A nice early spring bulb- Grecian Windflower, will have small sort of ferny leaves and early flowers, then goes away nicely before perennials fill out. Some Iris are very early and small. Snowdrops are very early.
Just trying to suggest some you don't have in the other bulb bed, and that won;t have too much foliage laying around for weeks.
If this is a sunny bed you might plant fall pansies and have them live thru winter, blooming whenever it is mild, and nicely in early spring till too hot or crowded out. (I do that every fall with a sunny bed)
Or get the pansies or johnny jump ups as soon as they are sold in spring. Or primrose sin spring.
