Sleeping beside the bed can offer useful information, but it does not automatically mean the location is wrong. The cat may like that area while preferring the floor's temperature, firmness or open space. Check whether the bed is too enclosed, has a high rim or offers less usable area than expected. Observe the behaviour at different times rather than moving the bed immediately after one nap. You could try a simpler permitted cushion arrangement or another appropriate position, changing one feature at a time. Do not put the cat into the bed every time they settle beside it. If the surrounding spot is already safe and comfortable, it can remain an acceptable resting choice. A purchased bed adds an option; its success should not require preventing the cat from using every nearby surface they happen to prefer.
Compare the two surfaces at the same time of day. A cat choosing a cool floor beside a thick cushion in the afternoon may make a different choice when the room is cooler at night.
For product comparisons alongside this advice, see Velvet Nest and Silver Velvet Nest. The details below explain their sizes and uses.
Further reading: cats.org.uk.
Velvet Nest
Silver Velvet Nest
AeroMat Chill Pad