Whenever I move a tank, I get large, clean rubbermaid type tubs. I drain the water into the tubs, using as many as I need to remove all the water. I put the fish into one of the tubs as soon as the water level is high enough that they are comfortable. I drop in an airstone. The filter and filter media and all gets dropped into the water of another tub or the fish tub if there is room. A lot depends on the size of the tank.
When the water is all drained from the tank, you can lift out the rocks, being careful not to drop any. I like to take a bucket of the "drained" cleaner water and scrub each rock off with a dedicated fish brush. If you scub each rock with a clean brush with used fish water, none of the beneficial bacteria that is on that rock will be harmed. It should be fine.
So much depends on how much beneficial bacteria you have in your filter and how much is "elsewhere". By and large, the better part is usually in the filter - that is where it has access to oxygen and all the ammonia/nitrite laden water as it flows through. If you just lift your filter off the tank and back onto the tank when it is moved and reset, you should really have no bump of the cycle. If your filter has very little platform for the bacteria and the majority of the beneficial bacteria lives on the rocks and tank walls, then you are going to have a bit more problem.
REmove all the rocks and all the water. Do not move a tank, no matter how small a move it is - even 1 foot - with ANYTHING in the tank. THis can cause uneven loading, resulting in a twist. Shearing motion, even a slight twist, can cause potential leaking down the road. It is not worth the risk. Empty the tank.
When you have your tank all moved and you are happy with its position, I usually add back in enough of the cleaner, used water that the fish can swim happily while you are resetting the tank. Place the rocks you wish to keep back on the tank floor. Fill the tank up about 1/2 the way with the cleaner used water, and then with new water - conditioned and all just as you would if you were doing a water change. That is exactly what you are doing, too. A nice water change.
Reset the filters, set it all going. If you have the majority or all of your cycle built in your filter you should not see any or very little bump in the cycle. If your tank is dependant upon the rocks as well as the filter, you will see a bump - possibly ammonia or nitrite or both for a few days. Usually this is a small bump and, with careful management and/or water changes, it will go away within a few days, also. Remember to test every day for a few days to make sure that nothing has slipped.
You will have moved your tank and all will be good. Do not be afraid to move things. I move mine around quite a bit. I also like to break a tank down and really scrub scrub scrub whenever the heavy algae gets so bad in the corners that it is unsightly. I preserve the filters and all is good. The tank is clean, the cycle never bumps and the fish look brighter, happier and I can