Can I clime Hakusan in one day

I like to sray in shirakawa-go and from there clime Mt. Haku.

Can I clime Mt. Haku in one day (up and Down)?

And can you recommen a suitable place to start (is there a bus to a path)?

If not possible, can you recommend a suitable day trip into the Mountains around shirakawa-go-

Thank you very much in advance.

Dorte

The only trailhead from which a day hike is possible for people who are in good shape (and start early in the morning) is Bettodeai on the Ishikawa side:
http://www.japan-guide.com/e/e4285.html

Bettodai is quite far away from Shirakawago, connected by a toll road that does not open until 7am from June to August and not even until 8am from September to November. That will not allow you a very early start which makes the day even more challenging. Needless to say: you would require a car to drive to Bettodeai:
http://www.japan-guide.com/e/e4286.html

If not possible, can you recommend a suitable day trip into the Mountains around shirakawa-go

The above mentioned toll road is quite spectacular, and there are a few shorter hikes that start at various points from the toll road. There is also the nice onsen with views onto the waterfall (see link above).

I just noticed that the toll road's closing hours would add additional pressure on completing the round trip within a day, especially in September and beyond when the hours are further reduced.

I definitely do not recommend it to 99% of tourists, but if you are very determined to climb the mountain, travel in summer, plan your trip well and are in very good shape, then it would theoretically be possible.