How often should I water these new shrubs?

As with any new plant, you need to keep it well watered until established. I would suggest water everyday, unless it rains (needs to be a good heavy shower at least).

The top one looks like Gazania, and therefore not a shrub (I could be wrong), but as it is likely to be perennial, will still need the same watering.

 

Every new plants want well water for growing.

 

Apart from the first week or so, to keep it alive!, I disagree with frequent watering. I think that regular watering makes the plant dependent on that supply of water, and encourages roots at the surface (where the water is provided) rather than growing roots downwards - where there will always be moisture, except in drought. Surface roots will be struggling by midday when the soil surface dries out in the sun ...

If soil is dry when I plant then I water the planting hole (to ensure that there is water under the plant). I water into the original rootball area to keep it "healthy" as it establishes, but I don't aim to do that for long (if we get a dry spell I need to water more/often, of course, to stop the plant getting stressed).

Thereafter I water heavily, but not frequently. Aim is to get soil moist around the plant, not to provide water directly to the plant. I might do this twice a week, but probably only once a week unless the plant is stressed, or we have hot / dry weather. Definitely NOT "little and often" but rather "lots and infrequently"

In a drought I would water 3 times a week - and probably once a week (in drought) for mature plants that won't manage easily on their own.

Your plants are mulched, the soil surface isn't going to dry out. Frequent watering may make the plants look healthy, but I don't think they will get established as well/quickly.