Hm well i've never had to hide them in a suitcase really, but i have other places (car, toolbox). Basically for any circumstance I hide them in a non-see through bag (i've used a small store shopping bag, and a small bag that holds my over-ear headphones), or some sort of secret thing to hide it in that looks unsuspicous but at the same time where no one else would look. (some sort of empty box used for medicine? hard vhs case (prob suspicious unless your going someplace with vcr lol) some sort of empty food container, like the box those powered drink mix things come in, something like that.) think of something that would work thats not suspicous, hides them well, and something someone else wouldnt look in or something, or maybe theres a "secret" place in your suitcase, or maybe you can even take the bottom panel out and hide them flat in a bag there. (not sure which uh, "product" you use out of the two, but if it's not the 'flat-shaped' ones then it might be even easier to find a conspicuous thing to hide them in).
as for disposing, i'm only practiced in secret disposing in the 'flat-shaped' ones because i only use those, which i use the wrapper from the new one im gonna use and wrap it up in that (i do it a certain way too so the edge's dont match the edges of the wrapper, therefore no 'red stuff' somehow leaking out on accident) then i sort of roll that up and then roll that up in toilet paper until i cant see anything through the TP (but dont wrap too neatly or anything, cause then it might look more suspicous. wrap the last couple wraps a big loosely so it looks more just like a used tissue or something) then place it in the trash bag down a bit like halfway through.
if you need to dispose of it in a different way (somewhere outside your room, in a public restroom) then get it all wrapped and prepared like i said, then shove it in your pocket (of course pay attention to where/how so there isnt tp hanging out of your pocket) or in front of your waistband then dispose of it in a trash somewhere else. or if in the public bathroom case, wash your hands, then when you use the paper towl to dry your hands sneak the "wrapped garbage" from wherever when you arent facing anyone or simply right when your up in front of the trash and throw them out together, or even wrap the product in the paper towel then throw it out. (as for the other 'product' you may use, the 'tube-shaped' one, i'm sure you can do the same method you just will need a lot more tp layers haha, or you could even bring in some paper towels or baggie to put it in than wrap it to prevent leakage.)
That was a long post haha, but hope it helps =)
oh and sorry for all the dumb nicknames for everything XD triggers my, and possibly others, dysphoria saying the real names for them.