That pale, stretchy look is basically your aloe screaming for light 😅 A bedroom shelf, especially if it's not right next to a window, just isn't bright enough. Aloe plants are desert succulents - they're built for intense sunlight, and when they don't get it, they literally reach upward and get pale trying to find it. The watering schedule sounds fine, so it's not a rot situation or anything scary like that.
Move it somewhere with direct sunlight - a south or west-facing windowsill is ideal, or even outside during warmer months if you can. You should see it start to firm up and get that deeper green back within a few weeks once it's getting proper light. The stretched-out parts won't suddenly shrink (that's just how they grew), but new growth will come in compact and colorful. If you can't find a super bright spot indoors, even a few hours of direct sun daily will make a huge difference compared to what it's getting on a bedroom shelf.
One thing though - if you do move it to bright light suddenly after being in low light for a while, ease it in over a week or so. Otherwise the leaves can get sunburned and turn orange or brown, which looks worse before it gets better 😬