I recently was reading a copy of "Woman's Day Encyclopedia of Cooking" (1965), which claimed the following (Vol. 1, pg 134):
Until quite recently, there was a close connection between baking and cleanliness. Our female ancestors had definite days for doing their chores, and Saturday was reserved for baking and baths. In an age when hot water did not simply come out of a faucet, the kitchen range provided not only the heat for baking everything from meats to cookies, but also the hot water needed for cleaning up for Sunday's churchgoing. The baking began Saturday morning, the baths Saturday afternoon
This struck me as a bit of an odd assertion. I would assume that cooking with heat happened multiple days of the week, and it sounded kind of like a "just-so" story.
I've done some initial searching, but I haven't found any other source describing this link, whether as rumor, fact, or myth. There's many references to bathing historically being a more difficult, time-consuming endeavor, and similarly many references to the general amount of effort required in food preparation. But I haven't found anything linking the two, particularly.
Was there a period, particularly somewhere in the 18th-20th centuries, in Western Europe or North America, where Saturday was considered both the day for bathing and also the day for baking?
If so, was the sharing of the day related to sharing a heat source?
If not, in the 1960's, was there some belief about history held then, but not as common today, that would lead to this assertion?
This isn't my specialty, so I'm not going to be able to answer the specific question with regards to baking and bathing, but I think you're making something of a false equivalency:
I would assume that cooking with heat happened multiple days of the week
Cooking and baking are two different things. You're absolutely right that cooking with heat (over a fire, on a stove, etc.) would happen quite often, but baking in the past could be quite a bit more involved.
Today we simply turn on the oven in our kitchen without thinking about it but, depending on the location and time period, even having an oven in the past might be a rarity: in medieval France, personal ovens were often illegal and all commoners had to use the communal oven belonging to their lord.
If one did have an oven (maybe a beehive oven in colonial America), heating it up, keeping it hot, and actually using it would be an all-day affair which had significant costs in both time and fuel. It could take 3-5 hours just for the wood to burn down to coals to keep the oven hot. This meant baking was a once-per-week event for most people; the week's bread (and maybe some other baked goods) would be baked all at once.
So baking happened once-per-week. Whether bathing coincided with that is another question that I'm not equipped to answer.