Try simply transferring the pet’s current bed to the suitcase.
If there is any way possible to make this work, turn to the pet’s current bedding first. The pet’s scent will create a more inviting, comfortable environment for your pet and increase the likelihood he will want to sleep in his new bed.
Shop for new bedding if the pet’s current bed doesn’t work with the suitcase design. Take measurements of the luggage’s inside before you shop. Hit the pet store first to find bedding that is comfortable but also designed to be laundered.
Another approach is to use an older pillow that you no longer sleep on, cover it with one of your old warm and cozy sweaters (wool or cashmere will be much appreciated) and then stuffed into the suitcase. Your pet will smell your odor and will appreciate the comfy pillow fill and the delicious texture of natural animal fibers. You could also try blankets that have your scent on them. That works as well.