This comes up quite a bit on the forum. Use the search function to see how people do it. It's way less complicated than anyone thinks. As someone who has done it a few times, I'm here to say it's also not as scary as anyone thinks.
Your critters will be fine in a bucket with an air pump. They'd honestly be fine without a pump. But since you have one, that's awesome. Just try to keep their temperature stable. Maybe wrap whatever container you're using in some insulated bubble wrap if you have it.
As for the tank? Drain it. Support any plants you don't want to damage. Support and secure any of your hardscape you're leaving in place. Use wadded up paper, bubble wrap, paper towels, paper towel tubes, wooden skewers, whatever you need that won't harm what's in your tank. Give it all a good mist and then seal it up with plastic wrap and tape it off.
If you can, bag up your filter media and fill it with your tank water. Keep that a decent temperature - just like your critters - and it'll likely be in good shape when you arrive. Even if it's been a couple days.
Don't worry about losing bacteria in your substrate. It'll be fine.
The longest I've taken is 5 days (I think) and everything has been fine. We're talking super-sensitive shrimp species and oddball sensitive fish. The worst that's ever happened is a slight ammonia spike with an old tank that lasted about 4 hours. Was easily fixed with Prime and a water change. That's one tank out of probably a hundred through the years.
If you can get some boards or a piece of plywood under the tank, that will make it easier to move and will allow for more support. Even if it's a small 10gal or something.
Don't overthink it. Just be more well-prepared and your tank will be fine.
