Waiting for them to eat something can be like waiting for a pot to boil. If you want to play with them maybe move over the present material to one side and add bedding and food to the new side or 1/4. You may want to remove some and start a second bin to safeguard the herd.

The peat moss really dried it up so I had to actually add some water. That stuff really holds the moisture nicely.

I mixed it all up for consistency and will wait to see what they do.

But, when I add new food, do I bury it? Or put it on top?

No puddle = not too wet. Worms love it wet. The worms weren't climbing the sides to escape wet conditions. More likely they were climbing because the sides were wet and they do that on wet surfaces. . . because they love it wet. The peat moss was totally unnecessary. It won't hurt, so not a mistake. Just not necessary. If your bin gets too dry, the activity will slow down. I am guessing its to conserve moisture.

If you put your scraps on top and don't bury at all, you will likely be dealing with lots of fruit flies. That's not a big deal outside, but if you are inside it can be a problem. Since you apparently leave your bin outside, you'll be fine with top feeding. Actually, it's better.

Worms eat according to a lot of variables. Two big ones are temperature and how easy the food is to eat. Keep the bin in the 70's for faster results. Lower temps mean less activity. New bins sometimes take a little while to get really active. It seems that sometimes worms need an adjustment period when any major changes occur in their environment.

Thanks for all the helpful info. I got it moist again. I'll leave them alone for a bit to let them adjust to the whole thing.

Instead of using peatmoss as bedding or to add when your bin gets too wet, you could just use shredded/torn newspaper/cardboard/corrugated cardboard.
When I add food to the bin, I also add shredded paper product on top of it. In summer to try to "smother" fruit fliesetc. and in winter to keep the heat in.
I would cover the bin with something to protect it from getting rained on, though.

You did the right thing by not feeding too much. That is how things can go wrong and eventually kill the worms. I keep a bucket with a big hole in the lid, lined with weed cloth. This is my pre-rot bucket(s) and the worms get it usually after 3-4 weeks.

I am not adding water, but it seems to be getting wetter. Still no puddle at the bottom, but very moist. And, the worms keep crawling up the side of the bin and into the space between the lid and the rim. Every time I open it, I need to sweep them all back in and collect the ones that fall off the lid as I open it.

Is there a way to encourage them not to climb up and out of the Rubbermaid bin?

You might want to drill some side holes above the compost level, you can always cover them with mesh. It will allow some convection going (warm air out the top, cooler air in from the sides) and more beathing. As long as the sides are dripping wet, the worms will explore even if they are happy.

As you noticed an inclosed bin seems to almost manufacture water out of thin air. As food breaks down it releases water and there's a ton of water in food. If you freeze food first and let it thaw, you can see how much you get out just from that. Either keep adding dry bedding to soak it up, or can do things like leaving the top off(do it while you're around to keep an eye on it) to let it really dry out a bit, or both. I prefer leaving it off (daytime or with the light on!) than just not tight as not tight can mean it's moist enough (and dark) for the worms to climb the sides and escape. With it totally off it dries out and the light is there so they no longer climb the sides.

With side vents I've also used a fan to blow air on the bin to help move air through the bin. That constant blow does a lot to remove moisture. Useful if you want to do it overnight and/or have some fruitfly or gnat issues and don't want to remove the lid.

You have to be careful about using too much peat moss. It needs to be a 50/50 mixture with something else like shredded paper.

Here is a link that might be useful: Worm Bedding

I'm with PeterK2. You need to add more holes. Ideally, there will be a lot of holes on the bottom. You can place the bin inside another bin or on the lid it came with to collect water that comes out. It's called leachate. If you're working it right, there won't be much water in the lid.

Here's why. Though worms sometimes eat the food directly, they mostly eat the bacteria that eat the food. The more oxygen you have going through the system, the more bacteria you'll have, the faster the growth of the worms will be. Hot air rises, so air will be sucked in to the holes on the bottom and pulled through the mass of VC. This is the main idea behind flow through bins and stacking bins. One source recommends 50 holes of 3/4" size. I didn't count when I added holes, but I added a lot. I started with smaller holes and they got blocked with muddy VC that dried out and it ruined the whole thing.

If you don't want holes on the bottom, you can put them about an inch above the bottom of the bin all the way around. You can put screening in to cover the holes, but it's not necessary. Very little VC falls through, even with 1" diameter holes. The worms can go through window screen if they want, so the screening won't stop the worms. The only time the worms will leave is if something's wrong with the environment. So if you have worms leaving, you have a problem. For me, the problem is usually overheating from adding too much food. Before I added the holes, the most common problem was pockets of anaerobic (REALLY stinky) VC. That hasn't happened since I added holes to the bottom.

As to your second question, the few times I've mixed the food in with the older VC, things have heated up badly and I've killed worms. I keep a couple of inches of moist, shredded newspaper on top and lift that up to add food to the top of the working area. Every couple of weeks, I add the food to the top of the newspaper and add more newspaper on top of that. This minimizes flying bugs. According to those who do this on a large scale and more scientifically, you're supposed to have 20x more bedding than food. I don't go that far, but basically, you can't have too much bedding.