It has been AGES since we looked at bunk beds, but in the ancient times they used to sell ladders, some were wood and heavy, substantial, others were much lighter, but still strong, aluminum maybe?????? (On Edit: They used to sell seperately as well as with a set of bunks. You could buy JUST the ladder.
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Go to a store that specializes in bunk beds (well, OK, there used to be stores that do that, are there still????) Ask them.
Not familiar with your unit, but it would seem if you get one small enough, and light enough that you could lay in on the lower bunk when you raised it, and just store it there on the bed. Again, not familiar with your unit, so maybe that is not a possible solution.
Good luck, post your solution here, we love reading about solutions!!