Shiretoko Hiking Time

I'm wondering if it's possible to hike around Shiretoko Goko as well as hike to Kamuiwakkayu Falls in one day.

According to the bus schedule I'll link below, the first bus from Shari to Shiretoko Goko is 8:10. I'd arrive at 9:35. The hiking course around all five lakes takes 90 minutes at best, so that's 11:00.

Japan-Guide says the hike to Kamuiwakkayu Falls takes 2-3 hours one way, so that's 6 hours round trip. I wouldn't get back to Shiretoko Goko until 17:00 and by then there's no more buses back to Shari.

Is it impossible for someone who is relying solely on public transportation to hike to Kamuiwakkayu Falls?

Also my Japanese friends keep telling me sightings of bears is more than never this year and I should avoid going to Shiretoko all together. Surely if that were true, they would close the trails, right?

http://sharibus.co.jp/pdf/2021_shiretokos2.pdf

Bear attacks are not exactly common, but there are usually a few that make the news each year as well as the dozens of others that don't make the headlines. As they are all over the country, they are not a reason to close hiking trails, it is more that people need to be aware of the bears and take precautions. If I was going to pick/head to one spot to see bears in the wild, it would be the Shiretoko National Park (although I have done some hiking in Nagano where "beware of the bear" signs were pretty obvious.
https://mainichi.jp/english/articles/20201022/p2a/00m/0na/022000c

Yeah, I've been hiking in Gifu and Nagano where there's a lot of bear aware signs. Friends never complained. But this year they're really pressuring me to not go.

Still wondering how to access the falls via public transport.

Yes, the bear warning signs I saw were up in Nagano. One of the other places with an unusual bear encounter was in Takayama - the warning announcement was unintelligible due to it echoing off the buildings, but in that case, the bear entered someone's house. I was fine, I am sure they would not have been able to use the elevator where I was due to their big paws.

As for the public transport, I have not looked at the bus timetables and access recently, but I did check some options for someone early this year for a possible trip into the national park. The most practical option I was investigating was to use one of the local guides in the area and their transport for the things they wanted to do.
Have you considered renting a car? Some rental places are very cheap - last car I rented was 1,600 yen for two days (overnight parking cost more), and I see one of my local places is less than 1,000 yen for one day. Might be more expensive up in Shiretoko, but worth a look.

last car I rented was 1,600 yen for two days
I have rented cars many times in Japan, never did I get such a low rate. Could it be a special promotion rate?

hike around Shiretoko Goko as well as hike to Kamuiwakkayu Falls in one day.
I visited both places in a day a few years ago. Initially, I was planning to use public transport, luckily I did not. I decided to rent a car, and it was a good decision.

sightings of bears is more than never
I encountered bears crossing the road on the way to Kamuiwakkayu Falls, luckily I was driving at that time.

last car I rented was 1,600 yen for two days 
I have rented cars many times in Japan, never have I been that lucky to get such a low rate. Could it be a special promotion?

hike around Shiretoko Goko as well as hike to Kamuiwakkayu Falls in one day.
I  managed to visit those places in a day from Abashiri a few years ago. Initially, I was planning to use public transport, luckily I did not. I agree with  JapanCustomTours, renting a car would be a better option.

sighting of bears is more than never
I encountered bears crossing the road on the way to Kamuiwakkayu Falls. I was driving in a car at that time.

Off topic, but I wanted to reply to the question on car rental:
last car I rented was 1,600 yen for two days
I have rented cars many times in Japan, never have I been that lucky to get such a low rate. Could it be a special promotion?
As far as I know, no, it was not a special rate. It was certainly not one of the major companies and a pretty small car, but sufficient for what was required for the two days driving around Kagoshima.
And, as a rate it was not exceptionally cheap given some of the offers/deals I see locally, but certainly lower than the last rental I had from Nippon RentalCar (but that included a one-way drop-off fee). As I mentioned, I can rent a car locally for less than 1,000 yen for a day (I think it was actually 880-yen) and the only other rate I bothered to remember off their rate chart was an option for renting a whole month at just 40,000 yen.

@Doc - did you see the following information?
https://www.goko.go.jp/index.html and
https://www.goko.go.jp/files/s_bus.pdf
I noticed there was a road to near the falls, so wondered if there was a taxi service that might operate (at least one way), and I saw the reference to the (limited time) shuttle. I would have expected you had seen it, so it might be a good option for at least one-way. Rental car would appear to be less of an option as access is restricted.
I also saw the Shiretoko Goko twitter feed keeps talking about the brown bears in the area and they have a large section in their FAQ regarding the bears.