You can orient your wood any way you like, if you're prepared for what happens when the wood dries and shrinks.
Bowls turned with grain parallel to the bed can work, if:
- the wood doesn't shrink much (yew comes to mind here)
- the wood is tough enough to build up tension without splitting (yew again, elm, black locust, honey locust)
- the wood is thin enough to bend instead of cracking (certainly less than 1/8", also depends on toughness)
what happens when drying is that the wood on the outside wants to shrink more than on the inside, because each fiber wants to shrink a certain amount and there's more fibers on the outside.
When that shrinking happens, either the outside cracks, or the inside moves (due to the form of bowls, most often down).
Here, flat teller-like bowls in yew dry without problems, even when 1/2" thick. An experiment in oak (20" diameter, 12" high, 1/8" thinkness) led to a nice crack from the rim right to the center of the bowl, from 3" wide at the rim to zero in the center. A walnut teller (16" diameter, 3" high, 1/4" think) led to 3 medium cracks in the middle, about 2" long, when the center moved downwards about 1" - meaning it now wobbles, and the cracks, while appearing small on the inside, are very much more ugly on the outside.
Flat bowls in black/honey locust have dried without problems, or with very small cracks (< 1/2" length) on the outside rim, in the sapwood.
I can only advise you to experiment - learning about wood and how it reacts depending on thickness, form, pattern etc. is one of the attractive parts about green wood turning.