If all you're moving is bettas, make it a water change and put them in solo cups, then right back into their tanks when you get them there. That is the safest and easiest way to do it. Please don't move tanks with water in them, that will break the glass. You can leave gravel in them wet, but be sure to drain all of the water. The way the water shifts when its move transfers pressure and weight to too small of an area and you end up with pressure cracks in the glass. If you want to save the water, put it in buckets, toss any plants into the buckets of water with lids on them, and then just refill everything when they get to the new home.
BTW, make sure the covers have some kind of small holes in them. The solo cups usually come with the little X cut out in the center... those don't need to be pushed open, as long as air can get in... you don't want a hole big enough for water to splash out or fish to jump through.