Sometimes when I have to fill a deeper bed, I buy bags of manure, garden soil, potting mix at half price for torn bags at Lowes. I don't know anything about steer manure, but I always buy cow manure both dehydrated and composted and haven't had any problems. I would recommend you find a source for vermiculite; it helps with keeping the soil loose. With what you have, I would add quite a bit more peat moss. Mel' mix is supposed to be 1/3 peat moss, 1/3 vermiculite and 1/3 compost ( as many different kinds as you can find: like leaf, mushroom, worm castings, manure).
Composting is nothing more than collecting vegetable material and letting it sit in a pile to decompose. There are all kinds of recipes. Check out lasagna composting and also the composting forum to get started, or the library for books on composting. If you have the energy you can chop and turn the compost to finish it faster.
Good luck,
Keski

I wouldn't worry about the steer manure. Fresh manure may contain e-coli but the stuff you buy in bags has been composted or dehydrated and won't be of any risk. I've used it before myself with no problems. Even if by some chance it wasn't composted properly and there was still e-coli present it can only survive in the soil for about 90 days. So by the time you harvest veggies in the fall there will be no risk. IT may have even been sitting in those bags for longer than 90 days. If you have some early veggies you'll be eating sooner just wash them well. No need to throw out all the soil.

The reason the potting soil says not for containers is that the garden soil mix will not drain as well. It's not such a big deal in the ground as all the existing soil, microbes,worms, roots, etc. allows for drainage but can become an issue in containers where the soil compacts and prevents proper drainage. Do your raised beds have a non-porous bottom (like wood or being constructed on top of cement)? If so you might have some drainage problems with that mix. If you bed were built on top of existing soil or lawn you'll be fine.

You could return the unopened bags and buy something intended for containers if you're really concerned. Adding vermiculite would also help (if you buy a container or potting type soil most often it'll already have vermiculite mixed in). You might also want to find some variety of manure if you can. Maybe return the other 2 bags of steer manure and try to find some other types. If that's all you have available then go ahead and use it.