According to my study, "change the bedding" seems bigger than "change the bed".
So, I asked Chatgpt
When you say "I change the bed every week," you are likely referring to changing the sheets, pillowcases, and possibly other items that directly touch the body, such as blankets or duvet covers.
When you say "I change the bedding every week," you are referring to a more comprehensive task that involves not only changing the sheets and pillowcases, but also possibly washing or replacing other items that are part of the bed, such as the mattress pad, bed skirt, or decorative shams. This phrase suggests a more thorough cleaning and maintenance of the entire bed.
But, from the information in the dictionaries, I think there is a simpler explanation. "Change the bed" might refer to change the sheet or the bed cover, but not blankets or pillow covers
and "change the bedding" might refer to change the sheet or the bed cover, and also blankets or pillow covers.
change a bed = change the sheets on a bed [=remove dirty sheets from a bed and replace them with clean ones]
bedding noun /ˈbedɪŋ/ /ˈbedɪŋ/ [uncountable] the sheets and covers that you put on a bed, and often also the mattress and the pillows
When do we say "I change the bed" and "I change the bedding"?