One time, I started on Shasta from the end of the road beyond Bunny Flat -- from the old ski bowl. That place provides a good spot to spend the night by the car to help acclimate, and starts 600' higher than BF. We went up the old ski bowl, then crossed over the ridge to the west a little below Helen Lake. Then we camped at Helen Lake.
It is always a zoo at Helen Lake -- lots of overnighters.
On Shasta, best time is late May and June. (Watch the weather!) Don't go in August -- too much snow is melted out, leaving an unpleasant rough rock climb and descent. When I tried it in August, all we could see from the summit was the tip of Mt Lassen. Everything else was hidden in forest fire smoke.
Crampons and ice axe use are the best on Shasta, and the glissade down to Helen Lake (sit on your butt and slide) is really fun.