I've taken bonsai classes, though I'm mostly a beginner, so feel free to use my advice as a jumping off point and do more research.
Bonsai pots, like Hazel commented, do have drainage holes, and they do have to be watered frequently. That's been my downfall with them and I'd recommend some kind of watering system on a timer if you aren't good about checking on the dryness on a regular basis.
So basically, bonsai is the art of training a young(-ish) tree and making it look like a tree that's lived hundreds of years and seen all kinds of storms, snow, ice, etc... There are multiple styles and you need to look at them and see which one is best for your tree.
Overall, the general rule tends to be that you want the first 1/3 of your trunk to be bare (again, there are exceptions based on style), then you start with your primary branches. As you move up the trunk, it should taper and the limbs should get smaller.
You can decide the size you want your bonsai to be an that will affect how you grow it out. I've seen bonsai on youtube that were micro sized and some that were massive.
You had a good idea that is frequently used when you try to grow a bonsai from seed. People will pot them, or even better, plant them in the ground to get much quicker growth. A bonsai should only go into a bonsai pot after you've gotten all the basic growth that you want. Bonsai soil is almost completely inorganic and some people prefer to grow in soil that is totally inorganic. So you aren't going to get a lot of growth after it's potted in a bonsai pot. I would repot this in it's own pot, or stick it in the ground and work on pruning it to get the desired structure you want.
Something to keep in mind is that if you want to thicken your trunk, you need more growth on top. Plants put on thickness to support further growth of the tree. If you cut it off, then your trunk won't thicken much more. Sometimes, people even leave undesirable branches growing low, to thicken the trunk before removing them. If you're happy with your trunk thickness, then it's time to start taking it down to size.
Stormy had some good points. It's unhealthy for a tree to have more than 1/3 of it's mass cut off at once. Some plants will survive it, but they're stressed and it takes them longer to recover from a massive cut back than if you did it gradually. This in bonsai, so you're in it for the long haul. I'd probably repot it now and then when it's recovered at the beginning of next spring when the new buds are starting to form, I'd prune it back by 1/3 or an inch above a node. Like you noticed when you pinched the top, it created back buds. There is a chemical in plants and when the tip of a growing branch is damaged or cut off, it sends it back down the trunk and creates back branching. That's what you want to occur. Then you'll be able to pick the branches that are stylistically best for you. Repeat this, cutting it back by 1/3, till you get it to the desired height.
Plan ahead and you can do a method where you make a small new branch the main leader by binding it upright. Some people cut the main trunk on an angle, notch it, and push the new leader into the notch before binding it. The idea is to cause the trunk to grow and trap the new leader. Keep researching and using methods like this to create the bonsai you're looking for. Keep in mind that the tree tends to determine the style. You can do a lot of manipulation, but it's better to pick a style that the tree already leans toward, instead of fighting it.
Also, while it make take you years to get really good at it and create a master piece, it's really not a hobby anyone should be afraid to get into. I suggest people do some research, watch some youtube, take a beginner class if ones available, but go out and buy some plants that look good and start giving it a go. Just like with any plants, I don't suggest that people get one and put all of their hopes into it. If you have a couple going, then if one dies on you, it's a loss, but not a devastating one. You can also compare and contrast. One can be your practice bonsai and the other can be the one you use what you learn on. I do recommend that you pick something like a shimpaku juniper, a box wood, or something similar that already has small leaves. Your ash has good sized leaves on it and this will throw off the look of the tree. You'll have a small tree with proportionally massive leaves. There are ways around this and people will defoliate the tree a try to cause it to always have small versions of the leaves, but as a beginner, I recommend something like the juniper that already has very small leaves. This is less work and stress for you. Good luck.