Long story short I have an invitation to stay with a buddy in Bishop, when are conditions the best at mammoth in terms of both skiing around the mountain and in the park?
anytime they have a good storm, they have a pretty good base now so anything that falls fresh will be nice, park is always good through may basically.
If you can roll on short notice, then wait for a big storm. We have a ton a variety in our terrain here and a pow day here is a great experience. Spring is great too we usually have enough snow for a bunch of really creative features in every park and corn skiing off the top is pretty close to unbeatable. Another advantage to the spring is that it's light later and you could ski all day at the resort and still get some good backcountry in before the sun sets. There's lots of good and accessible boot packs in the area that are great in the late afternoon.
the answer is late march: deepest base and nice spring weather
I've had great conditions and really shitty conditions (damn ass atmospheric river) mid winter there. Spring time is a guaranteed good time, one of the best places to be once may rolls around.