You didn’t say what kind of bear – smallish black bear, big black bear, inland grizzly, coastal grizzly (brown/Kodiak bear) – Lots of bear threads and opinions.
The 329 is a very specialized handgun. Unless you are a pretty seasoned hangunner, it is extremely hard to shoot accurately. Some guns exhibit sticky extraction with standard factory .44 Mag ammo. If you gun is one of these, try different ammo or better yet send it back to S&W (under warranty) and have them fix it. If the “lock” is going to be an issue, it will happen with these guns. Also, some have short firing pins (weak primer strikes) with resulting erratic ignition. The light weight 329 is also a notorious bullet puller (crimp jump). ALL OF THE ABOVE REQUIRE THAT YOU TEST YOUR CHOOSEN AMMO AS IF YOUR LIFE DEPENDS ON IT – IT DOES.
With that in mind.
No Ammo Designated +P in the 329.
I’m a hand loader, so I can’t speak to cost effective factory available “minor” .44 mags or .44 specials.
Here are some .44 mag ammo that should be fine in the 329PD.
Any standard .44 mag ammo from Hornady, Speer, Federal, Winchester, Remington, Barnes, HSM, to mention a few.
Also boutique makers such as the following – Just make sure you read the descriptions – they will tell you what guns their ammo is made for.
If it was me and I was going to use a 300gr+ bullet in the 329, I would choose the Garrett Defender (the mild one), or the HSM Bear load -- although you won’t like the recoil in the 329.
Buffalo Bore
https://www.buffalobore.com/index.php?l=product_list&c=10
Garrett Cartridges
Garrett Cartridges Inc.
Underwood
https://www.underwoodammo.com/44-remington-magnum/
Double Tap
44 Magnum
FWIW,
Paul