What kind of shrubs?

Where do you live?

What is growing in the rest of the garden?

Roses

Southern California (Riverside - 60 miles east of Los Angeles); USDA zone 9b; Sunset zone 18)

Nothing (I do not want to encourage weeds)

Lay organic matter on top of the soil without disturbing that soil so you don't stir up weed seeds

What you call "weeds" (unwanted plant growth) will grow anywhere steps are not taken to keep them under control. Many of these "weeds" can be indictor plants, telling us about problems with the soil it we pay attention and read them, and many of those "weeds" are wild flowers.

Improving the soil should begin with a good reliable soil test so one would know the soils pH and major nutrient balance as well as the amount of organic matter in the soil so the existing shrubs can grow in a healthy environment. Adding organic matter, in the form of mulches, will help keep any unwanted plant growth under control, but will not totally eliminate them. Mulches can help suppress unwanted plant growth, help maintain soil moisture levels, help keep soil temperatures moderate, and add organic matter to the soil, but they will also create conditions that may allow unwanted plant growth.