I've never used body paint, but from what I understand of it, it's a texture painting application, so you would use it to paint a texture on an imported obj, export the texture from body paint as a jpg file and then apply the texture to your figure in Poser or DAZ Studio (Consult the Poser/DS help doco for info on how to apply textures).  At that point you should be able to import it to Bryce without any trouble.  You can paint and apply the texture at any time, before or after you animate the figure.  You can even apply it in Bryce after you've done the import if you want.

Personally, I'd go for Vue rather than Bryce for importing and rendering Poser animations, but Bryce is certainly a lot cheaper so it depends on your budget.

If you have a few dollars to burn and you want to save yourself a heap of time and effort, you might take a look through the marketplace and see if there are any texture sets available that will meet your needs without you having to paint your own textures in body paint.  It sounds like you are just at the beginning of your Poser learning curve, so make sure anything you buy is compatible with the particular figure you want to use it on.

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