1. Configure your TFTP server (on host computer)
2. Put your new u-boot binary image into the server directory (usually /tftpboot)
3. Configure your target (Shiva):
   setenv serverip <your server IP>
   setenv ipaddr <Shiva box IP>
   setenv gatewayip <empty if you do not need it>
   saveenv
4. Now you can use "bubt". You should provide the image name to bubt command or rename the image in TFTP server directory to the default one.
5. You do not need to re-install u-boot if you only want to replace the filesystem.
6. I would start to build the filesystem using NFS exported directory and then when satisfied with the result, move it to flash

I personally run NBD server on my NAS. That allows me to "swap over the network". It might be not the fastest swap ever, but on some low-memory embedded systems sometimes you need more memory then generally available - for instance for locales generation or native compilations. I saw "memory exhausted" message on boards with 64M RAM when desided to add some swap space. However with Shiva's 512M you may not need one.

I believe you will not be able to mount root on USB stick without initrd image. Which instructions did you followed by?

bubt is the u-boot command used for replacing the u-boot image itself, not the kernel/filesystem image. Probably this is not what are you trying to do.

What kind of enclosure - bus or mains powered?