If you want to try to sprout your chinese elm seeds, that is a worthy project. But I agree with tom, that is not a way to get to have a bonsai tree in this lifetime. There's a bonsai guideline that says your finished bonsai should not be taller than six times the diameter of the trunk. Once you have reduced the root system and put the tree in a tiny pot, that trunk is not going to thicken up appreciably. So in order to have a six inch tall bonsai, you need to grow your tree in the ground until the trunk is an inch in diameter, at which point it will be a fairly tall tree. Then you dig it up and chop it down and start turning it in to a bonsai. (Shortened version of the process!)
If you want a bonsai now, check nurseries for mark down trees/shrubs. At the end of the season, they practically give away unsold stuff. Look at your own yard for what has bonsai potential. Check construction sites and road edges....
OR buy yourself a bonsai in training or pre-bonsai tree. These are trees that are in nursery pots that have been given just an initial rough shaping. They are a lot cheaper than finished bonsai and it will be your tree, because you will do more of the design and training of it.
Weluma has a nice selection of pre-bonsai trees, mostly in a price range of $10 - $30:
https://us.weluma.com/search/?q=Pre%20Bo ... gQodcUUJvQ
Wigert's bonsai also has a big selection of pre-bonsai trees:
https://wigertsbonsai.com/store/index.ph ... x&cPath=66 also bonsai of brooklyn:
https://wigertsbonsai.com/store/index.ph ... x&cPath=66 and many others