And here's another picture

mp,

A couple questions to get a better picture of what is happening with the system design. The soil doesn't look too sandy where the mulch is gone. So the water should spread out in the soil laterally. The placement of the lines looks okay. It should be over the roots ball not next to the trunk of the plants.
Question:
1. What is your water source pressure(psi) and flow rate(gpm)?
2. Is there a pressure regulator on the drip system?
3. What is the flow rate per linear foot of tube and pressure rating of the drip tube?
4. What type is the tube(surface or subsurface)?

Shouldn't take that long to have water spread out in the soil.

Covering with mulch is only cosmetic and does not help with distribution and worse you can't see if any of it is clogged.

I would have gone with small pop-up sprinklers which you can see and hear if they are working and are virtually invisible when not in use. They work better in mulch as well.
But they do need flow and good pressure to operate. Didn't want to hear that did you. JMHO Aloha

Thanks for the reply @lehua13:

1) water pressure is 55 psi, the emitters should be 1 gal. per hour each
2) I'm not sure if there's a pressure regulator or not. We had this installed in addition to a full yard system, and there are all kind of valve boxes and things throughout the yard. If there is one, I don't know how to identify it.
3) I don't know the answer to this - it is the same kind of tubing I see all around in commercial landscapes.
4) I don't know for sure, but I believe it can be either. Contractor told me I didn't have to bury them, but they could be buried. FYI - the little parkway strip of grass was too narrowfor pop-up heads, so they installed these same drip tubes, but buried underneath the grass.

Regarding pop-up sprinkle alternatives - the contractor told me that all new systems in our county have to use drip in flower beds because of our severe heat and common water restrictions.

So what do you think? After spot checking with a spade some spots around each bush are farily wet and some are still fairly dry. Is this a design problem? A pressure problem? Should I just run it longer?

Feel the tube, it should be fairly hard. Also lift up on the tube so you can see if it is dripping. There should be a constant drip, drip drip. From the pic's it appears that there is plenty of drip line for that small area and the spacing of the lines is not stretched out. There should be plenty of water there. Rake back the mulch and see if the wetted area is spreading out under the mulch. The emitter spacing on the lines appears to be close (12"-18") so if designed properly that area should get wet in not too long of time. Is it wetter closer to the valve then at a more distant point, if so there just may be too much drip line (gpm) on the zone. That looks like Netafim drip with a check valve in the emmitter. If your lacking pressure they do not drip properly. 1 gph is a pretty fast application rate and unless it is a sandy soil that dirt should get pretty wet pretty quick. If the run is real long and you have, for example a 20 psi reg on it there may not be enough pressure at the far end to operate properly. We most often use .6 gphx18" spacing and in 2 hours time there is most definitely a visual wetted area. From your description and pic,s, if I had to guess,too many gpm, low pressure.

mp,

Your installer should be able to answer the questions you can't. homr is correct, it looks like a pressure problem that your pressure regulated orifices are not putting out properly. Also this type is prevalent to clogging if the water is not very clean or their was a break in the line and not flushed. Check your source pressure or ask the installer what it was. JMHO Aloha