Both names have been used for Laurus nobilis.

Sweet bay bush might refer to sweet bay trees/magnolia virginiana. They're trees down here, but I hear they're only bushes up north.
Sherry

THANK YOU,bboy and misssherry. I ran out of room on my last post,but was wondering how to care for it. What kind of pests and disease to expect. What to do about them and how big do they have to get before starting to harvest leaves. I make pot pourri and plan to use some leaves in a few of my mixtures. Any info I can get about this plant would be greatly appreciated.

Since you're planning to use it for potpourri, it must be laurus nobilis, which is related to our native redbays/perseas - the leaves from both smell heavenly! I don't have a clue about how to grow l. nobilis - sorry.
Sherry

Find the place you want this and plant, it may grow slowly but can get quite large, it is very hardy but may not like being transplanted once established .

Can you show us a photograph of this plant? It seems to me that the id is still not certain. If it was sold as 'sweet bay bush' it may not be Laurus nobilis which is simply called a bay tree over here or bay laurel in the States, I believe. The fact that it was labelled 'bush' arouses my suspicions.

Thanks to all. I get the feeling that bush and tree are the same. The lady I bought it from said it was a bush. Maybe because it wasn'nt as big as a tree yet. I love this plant! The leaves and stems are so fragrent. I will do anything I can do to make it thrive. I'll send some pictures as soon as I figure out how to do it. I think you're right mudflapper I'm going to keep it right where it is. I might get a new tree and harvest from it while waiting for this little one to grow. Still no clue as to pests and disease to expect. Any ideas?

If the leaves smell that good, then it can't be magnolia virginiana - m. virginiana leaves have a slightly good smell, but never powerful, at least not here.
Redbay/persea borbonia and swampbay/p. palustris grow wild on my property - their leaves have a powerfully wonderful smell, and they're closely related to l. nobilis. Since perseas here get very ugly redbay galls - p. borbonia more than p. palustris - your bush might also. These are called psyllid galls and are caused by the insect trioza magnoliae. Perseas are also the host plant for palamedes swallowtails, which also occur in Florida. So you might find a palamedes caterpillar on your tree/bush. Here's an early instar palamedes caterpillar -
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And here's a late instar (older) caterpillar -
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And here's an adult butterfly -
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I don't know what you can do about the galls, if you get any - I can't find any literature that tells what you can spray on the trees that'll kill the psyllids without killing the butterflies. If I were you, I'd let the caterpillars eat the leaves or move them to a local redbay/swampbay/silkbay.
Sherry

If "very hardy" was a reference to cold tolerance of Laurus nobilis it is actually rather subject to frost injury.

Some common names for this are Bay Laurel, Apollo's Laurel, Roman Laurel, Grecian Laurel, Poet's Laurel, Sweet Laurel, Royal Bay and Sweet Bay.

Magnolia virginiana has been called Sweet Bay (Sweet Bay Magnolia), Silver Bay, White Laurel, Beaver Tree (Beaverwood), Swamp Laurel, Swamp Sassafras, White Bay, Swamp Bay...

It might be interesting to note that Red Bay (Persea borbonia) has been nearly decimated from native forests in SC, Florida, Georgia, and other southern states.

Attached is a bulletin from Hunting Island, SC (Beaufort), my home for many years. You can find out if the problem has been introduced into your areas by contacting your state forestry departments.

Here is a link that might be useful: Click here

The redbay situation is so disturbing for us butterfly lovers!
I've ordered and planted many other closely related members of the laurel family from various parts of Asia to see if palamedes swallowtails would lay eggs on any of them - so far they haven't. If the insect that spreads the disease makes it here - and so far it hasn't, knock on wood! - it would be nice if I knew of an alternate host that hopefully would be resistant. They might use sassafras, which would solve the problem, provided sassafras isn't susceptible to the same disease. I know palamedes caterpillars will eat sassafras leaves, because they've done just that when I raised spicebush and palamedes swallowtails together in the same cage. I've never found any cats on sassafras, though, so as far as I know, they don't lay eggs on it.
My latest new laurel is bog spicebush, a rare shrub that is native to my immediate area. I'm hoping that spicebush swallowtails and/or palamedes swallowtails will use it - the greater the variety of host plants you have, the better.
I got these bushes from Woodlander's in SC, Rhizo - I think you know the original owner.
Sherry

I have a bay leaf tree/bush in my back yard. I live in the Seattle area. It grows like crazy. I cut it back, taking off about 8 feet in hight, and it has grown back about 4 feet of that since last spring when I did cut it.

My question is: Can it be dug up and replanted into another spot? Not that I want to keep it, but I want to offer it to someone who would like it.