@Roygee - rendering as 360° panorama won’t help you because you get a cylindrical panorama, not a spherical one as needed in Carrara. This cannot be done in Bryce directly except with the Bryce 7 Pro Spherical Mapper (http://www.daz3d.com/bryce-7-pro-spherical-mapper).
You can render the 6 cube faces (best result) or the two hemispheres. The mirror ball is the most complicated. You will need a program to assemble the individual renders and create a spherical (or equirectangular) projection.
As TheSavage64 proposed, do not save each render but EXPORT the rendered images as *.hdr. Now assembling the renders to a spherical HDRI, you need an HDRI capable graphics program to do so. I would assemble the renders (cube faces) to a vertical cross in Photoshop CS2 or newer, then save the cross as HDR file. With HDRShop, you can open this vertical cross and transform it to spherical. Of course, the spherical mapper renders the scene directly in the spherical projection and if exported as *.hdr out of Brycce, you’re set.
Yes, the tutorials were made for Bryce 6.1, there was no hdr export then. It came with Bryce 7.1 Pro. Also saving a sky as HDRI came only with Bryce 7.1 and you need the Pro version, in the Standard and PLE versions, this option (among others) is disabled.
If you export a rendered image as hdr, it is a true 96 bit per pixel file. But you do not have the high dynamic range you would expect in an image with the sun and deep shadows. What you get is a very finely shaded image with more than the 8 bits per colour per pixel as we get with a LDRI (bmp). Nevertheless, it is of higer quality and will emit nice ambient light.
You can use Bryce to render a scene that can be made ro a true HDRI with very bright light sources and all you expect from an HDRI for IBL. However, this is a tedious and tricky thing to do. I have a 3-part video ready that shows exactly how this is done, but the video is not yet published. The video was done exactly for those who want to create a real high dynamic range panorama in Bryce for using it for IBL in Carrara or Studio (and Bryce).
If your image is to be rendered as backdrop, you have to render it quite large. I have a calculator on my website (see sig) which helps you determining the document size needed. Go to Science > Panorama. If you use it as backdrop in Carrara, be aware that Carrara tone-maps it linearly, it cannot tone-map it with a more sophisticated tone-mapping operator as is built in in Bryce.
As for using it in Bryce - memory is the issue because Bryce is still a 32-bit application and cannot directly address more than 2 GB. And Bryce does everything in memory and cannot bleed over to a HD. If you install LAA, you can go up to about 3.5 GB and can load a light probe up to 6400 pixels diameter, else, much smaller. Bryce, by the way, prefers the panoramic HDRI on the angular projection. David and myself have developed a lens for Bryce, the Bryce 7 Pro Scene Converter (http://www.daz3d.com/bryce-7-pro-scene-converter) which accomplishes this in one go. But this projection cannot be used in Carrara.
I think that’s enough for a start. If you have more question, do not hesitate to bring them forward.