High end point-and-shoot, bridge camera, or intro-level DSLR?

I think its obvious you have figured out the limitations of point and shoots, so take that off the table.

Bridge cameras are glorified point and shoots, you're still stuck with the lens attached. The quality may be better, but in all honesty they are point and shoots that start to look like a DSLR camera.

Since your shooting manually, I think it would be a wise choice and start to get into the DSLR way of thinking. You'll find the basic quality to be better, with a lot more options. Getting into DSLR photography gives you higher ISO, faster shutters, and with good lenses the ability to shoot in more difficult conditions.

Drawbacks are numerous, the cameras are bigger and heavier, cost more and you'll need lenses. If you have three lenses and the camera body, suddenly you can't just grab the camera and go take a pictures, you'll need a way to carry it all. It has the added problem of stifling going out and shooting if it becomes this big deal of packing and carrying all that stuff. Most people though know what they are going out to shoot and may just carry one lens. That's not to bad, but the cameras are still to big to put in a pocket.

A few things that are important to know is that one: Camera bodies die/get old, but lenses don't as easily. That means you may have a lens for 20 or or more years, but go through eight bodies in the same time. The effect of this means that you have to go with a particular company for all those years. Nikon people tend to be Nikon buyers for decades, and so on with Canon and perhaps other companies. If you see a great new camera that Canon came out with, but you own Nikon lenses, well your out of luck. However that is not such a bad thing, the way things work is that both Nikon and Canon do this little fight thing. For six months or so one of the two will ramp up and release all this wonderful new gear, everyone gets all excited while the other releases nothing or little. Time passes for a year or whatever, then the other company starts releasing all their new stuff, everyone gets all pumped up again. Right now we are in the phase of Nikon, but its on the tail end. In the end it doesn't matter, both companies make great stuff.

Two: There is cheap consumer glass and professional glass (glass is the same thing as a lens). When pricing glass the most important thing to look for is the lowest f-stop. the lower the number the better. Sometimes you may be in a situation where the light isn't very good (happens all the time), and in order to get the shutter an a minimum speed like 1/60 to prevent blurry photo's you need to open up the aperture. If your lens isn't capable of opening up that much, you'll never get the shot. Your at the physical limitation of the camera. You can boost the ISO, but that introduces noise, and you'll pay dearly for not having a lens that can open up a lot. We call a lens that opens up a lot a fast lens, because you can use a faster shutter speed and not get blurry photos. Fast lenses are f2.8 or lower. Fast glass is more costly, the faster it is, the pricer it gets. If you see lens you like, but has a aperture like f4, its slow glass, and it will make your life miserable. The exception to this is very long glass like a 600mm that is impractical for speeds like 2.8 (relax that is high pro stuff that is 10 thousand bucks).

I'm probably getting in it to deep for your needs, but honestly if your shooting in manual and want to improve the basic quality, its time to go DSLR.

There is a considerable range of prices for these cameras, I do not recommend anything in the D3000 (Nikon) price range. Its too much of a hassle to deal with, you don't necessarily have autofocus and some other things that you'll want. Go a little higher like D5000, or maybe a D7000, its actually more like a D7100 etc… If you can swing it I recommend a D90.

Choose a camera that you like and feels good in your hands, there is very little difference in the long run whether you choose Nikon or Canon.

It sounds to me like you've been ready for a dSLR for a while. Keep your Powershot around, you won't want to lug a dSLR all the time but I'd say it's time for you to step up. As for which brand you'll have to decide. Go to a store and try a few models out. You'll see a pattern, Canon's menus are pretty similar to other Canon menus, Nikons are similar to other Nikons, etc... Once you figure out the brand you can go from there. There are great cameras from many different manufacturers. You may even decide to go away from Canon if the menus and controls on your current camera seemed to irk you.