Since its a form of plastic how about a glowing red hot nickchrome wire. It will probably smell really bad though.I would go with a band saw first.
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What is a nickchrome wire?
bad spelling http://en.wikipedia.org/wiki/NichromeNichrome is a non-magnetic alloy of nickel, chromium, and often iron, usually used as a resistance wire. Patented in 1905, it is the oldest documented form of resistance heating alloy. A common alloy is 80% nickel and 20% chromium, by mass, but there are many others to accommodate various applications. It is silvery-grey in colour, is corrosion-resistant, and has a high melting point of about 1400 °C (2552 °F). Due to its relatively high electrical resistivity and resistance to oxidation at high temperatures, it is widely used in electric heating elements, such as in hair dryers, electric ovens, soldering iron, toasters, and even electronic cigarettes. Typically, Nichrome is wound in coils to a certain electrical resistance, and current is passed through to produce heat.
A bandsaw is a REALLY DANGEROUS way to cut a round object without extreme care.
Actually, it wasn't dangerous at all. It is indeed dangerous to cut some round things, but a bowling ball's plastic is relatively soft, and the blade didn't try to grab and sling like with some materials. Just go slow and keep your fingers out of the way.
I would think that goes for any of the mentioned power saw methods.
I have some experience of trying it. Fortunately I wasn't using a fast saw, and I was expecting something nasty to happen.
I cut one in half a few years ago using a bandsaw. Wasn't difficult at all.
I've cut one in half with an ordinary hand saw used for timber. It's the way I also cut PVC pipe, conduit etc. It works ok on most plastics and worked well on the bowling ball. The inside was full of a kind of rubber/cork mixture, and has a strange smell.
Hand saw the ball will spin on the band saw unless you can hold it really well. This would requite making a container for the ball and cutting through both.it's plastic all it will take is time.
Chainsaw, bow saw, tree felling saw, big bandsaw, Score it deeply all around with a table saw and finish the cut with a handsaw, entire cut by handsaw,
You forgot giant death laser from James Bond.
Everyone's suggestions are great so far; I'm thinking spindle mode on a lathe, at least to get you started, then any old saw would do.