No, a sleeping bag is not essential and you can absolutely do without one: in all the facilities that hosted me, hostels and masserias included, I always found sheets, pillowcases and blankets included in the price or available for a small additional fee that is certainly worth the lightening of your backpack. I mistakenly brought a sleeping bag, but it was useless baggage that accompanied me for all 340 kilometers from Bari to Alberobello. I was ready to have to use it at least at Masseria Galietti, a donation-based facility that from the description seemed to have only sparse camp beds (while the sheets were definitely there) or in some B&Bs that charge extra for bedding. If you doubt whether the facility is equipped with bedding or not, just ask beforehand (which I, for example, did not do in the case of the masseria) and pay those two or three euros extra when you have the option of getting a bed without sheets. It’s not worth being stingy for such a short walk: the way I see it, it’s much better to lighten your backpack and sleep every night within fresh-smelling sheets.