I attempted to use bobcat back in the 90's with my XT...even then, it wasn't so usable for browsing web pages. I didn't take long to switch over to a Telnet client and a shell account on Grex, which is a public-access UNIX box in Ann Arbor, MI. They're still up and running, and provide mostly text-based services including e-mail accessible by a number of text-only clients (I prefer pine/alpine). You can of course use the Lynx (related to Bobcat) or Links browsers from the command line, and if you're using a terminal client for the XT that supports X/Y/Zmodem or Kermit, you can transfer files downloaded from the web directly to your XT.
I'd recommend checking out Mike Brutman's mTCP package...good DOS utilities for connecting to TCP/IP services, and they're /intended/ for use on really old PC-compatibles.