As an aside, 'Forest School' is a term for a particular type of outdoor education, focusing on six principles and can be delivered only by a qualified Forest School Leader. Anything else is just "outdoor learning".
Anyway, half days won't work. First because there wouldn't be time to clean properly between shifts (either three cleaners have to clean all the classrooms and toilets in 45-60 mins or the teachers have to do their own and lose out on a lunch break). Second, because there's a reason we teach the core subjects of Maths and Literacy in the morning and foundation subjects like art in the afternoon - children are much more focused in the mornings. So the afternoon cohort would have to leave their TVs and tablets, have lunch and then come in for 2-3 hours of learning. It isn't going to happen.
Whole days are much better: two days in, deep clean, two days in.
However, this whole thing about having a "bubble" doesn't work. If children are not in full time, each class will have two bubbles, requiring two teachers. Otherwise the one teacher is potentially spreading the virus from one bubble to the next. Also, the children with siblings will mean their family are in two or more separate bubbles. The bubbles are separate in school but mix at home through siblings, then back to the bubble.
Perhaps have family bubbles instead? Each classroom has 15 children filled with siblings from across the year groups. So potentially only having five or six different families mixing. They do the online learning set by their teacher (who is in school with one bubble two days a week and setting and marking proper remote learning the other days) with an adult available to help if need be.
They could even do three days a week for each bubble, with week A having bubble 1 from Miss X's class in Mon-Wed and week B that bubble is only in Mon and Tues. Big cleans would happen after school after that bubble has had their two or three days.