A family member brought over leaves of a cactus and told me to just plant them in soil. How long should it take to bloom from leaves? She said they get pretty big and to transplant them when they become too big for their pots. She also said they are very rooty plants that disturbing the roots won't kill it, is that also true? I'm a rose person my self and haven't one house plant except a chinese bambo plant, or also known as a lucky bambo. Any help would be greatly appreciated. Many thanks.

Use a somewhat small pot with enough room for all the cuttings to fit down in the soil. Make sure the soil is fast draining and let it dry between waterings. Keep in bright indirect light (no direct sun)
It will be a while before you see any flowers, the roots need to fill the pot. They are slow growers, so I wouldn't worry about it getting big in a hurry, anyway, the stems can be trimmed back to a manageable size when it does.
Disturbing roots of any plant should be avoided if possible, but it can be done with no problems as well if it's not over-potted (pot too big) The Christmas cactus can stay in the same pot for years.
Cool nights and shorter daylight hours in the fall bring on buds.
Only feed when fully rooted in the spring and summer months, stop when you see buds in the fall.