Possibly depends on the type of tree the bark is from and maybe how finely it's shredded since you say it packs down. I use shredded bark mulch that is from a log home builder and is likely Douglas fir and spruce. I have no problem with water not penetrating.

Perhaps in a small area you could add some pine bark chips and mix them a bit with the shredded mulch. See if that works before removing all the mulch.

Any substance can be somewhat hydrophobic, water repelling, when one first applies water. It may take several minutes of wetting for that water to flow through that material. Keep wetting until the water flows through.

Yep, mulch mat sometimes happens with the fine stuff. Your best bet is to break it up/work it once-twice a month or more with a hard rake and improve its air circulation. Perhaps stop adding more till this breaks down and starts to expose the soil layer; then add a different product. Your mulch layer may be too thick, too dry, or it may be just the nature of the product as it breaks down (sometimes forming a hydrophobic mat of mycelium). Here is a site which explains some things:

http://www.clemson.edu/extension/hgic/plants/other/compost_mulch/hgic1604.html

If you want to go to another type of mulch, my thinking is to let your stuff break down till you start to see your soil or you know that itâÂÂs broken down and thin enough so as to add another product on top or work into the existing.

This season I am using a double ground - aged bark and wood fibers mulch (non -pallet wood) which I need to rake for aeration. ItâÂÂs meant to break down in one season leaving a layer of nutrient-rich organic matter to work into the soil. I will add another product on top after it decomposes and becomes better aerated. Right now itâÂÂs still fresh and the water takes time to get through this finely grounded material to the soil, so I left it thinner around the drip edges of my plants; not touching the base of the plants. Past seasons I have used course natural wood chips, shredded pine bark mulch, shredded hardwood bark mulch, cedar mulch, and aged free mulch from local tree service companies (got to watch for problem insects and diseases). I had to rake and break the shredded and the free aged stuff which was partially finely broken down, but not the course chips. I have not used pine bark nuggets but it seems those would need minor attention. Stay away from colored products and recycled pallet mulch. Some pallets may be from other countries like China containing mystery wood and treated with who knows what.