15th October 2009
I have re-written this first post to show where this thread is at and the bonjour options available for Snow Leopard..

To outline, I use the GA-EP45-DS3L which uses the Realtek 8111C Chipset and I started this thread back in August as I couldn't get Bonjour networking functioning with the RealtekR1000.kext from /Extra with the kernel running in either 32-bit an 64-bit mode. I build my systems without touching the retail install and anything I need to add for my system goes in to Chameleon's /Extra folder.

LATEST!
Bonjour now confirmed as working from S/L/E with a 64-bit kext developed by Bit Shoveler and now wrapped in to an auto-installer by Weaksauce12.

There have been reports of using this kext can result in your networking taking a performance hit. If this is the case then see this post by RickyTan.

I can now say that for me either of the following options work:
• Sonotone's package installer to automatically install Daniel U Becker's ifconfig and a startupitem to run it when booting.
• Adding Bitshovelers RealtekR1000SL.kext in to /E/E along with IONetworkingFamily.kext from /S/L/E, in to /E/E. For this option to work, you need to edit each of the kext's info.plist and change the OSBundleRequired key/string from Network-Root to Root. (Thanks d00d).

Previous status...
Bonjour with Realtek driver works ONLY with the kernel running in 32-bit mode.
Attempts to contact Realtek via email for a 64-bit driver have been made.
Bonjour works with the ifconfig method with the kernel running in both 32-bit & 64-bit mode.


Timeline of solutions in this thread (Ordered by most recent first)

3rd November 2009
NEW - Weaksauce12 has confirmed Bit Shoveler's 64-bit kext as working and has wrapped the kext in to an auto installer.

3rd November 2009
Z4g0r brought to my attention that Bit Shoveler has developed a 64-bit Realtek Snow Leopard kext. Which I tried from E/E but couldn't get it to work.

29th October 2009
Sonotone has put togther a package installer for installing ifconfig and a startupitem so you no longer need to store your password as plaintext. It also has the option of installing for your adapter on en0, en1 or en2.

27th October 2009
Weaksauce12 wrapped the ifconfig command & Scorcho's applescript in to an application, which after an initial edit, can be added in to the Applications folder and set to auto run at login.

1st September 2009
Eliade created and posted a script using LoginHook to allow ifconfig to be run from startup.

31st August 2009
Scorcho created and posted an applescript to allow ifconfig to be run from startup.

31st August 2009
ifconfig Workaround works with Snow Leopard with the kernel running both 32-bit & 64-bit mode.
Thorias posted a workaround by Daniel U. Becker which uses a rebuilt ifconfig command to force the NIC in to promiscuous mode. Note: you can't use ifconfig supplied by Apple, you need this rebuilt version. Run it with the command in the Read Me and it will activate Bonjour Networking with the kernel in both 32bit & 64bit mode.
Incase the original webpage ever goes offline, I have saved Daniel U. Becker's webpage as a webarchive along with the original binary and sources, zipped it up and posted it below.

30th August 2009
New Realtek drivers: RTGNICv2.0.3.pkg work with Snow Leopard with the kernel running in 32-bit mode only.
Markus23 posted a link to the new Realtek drivers and gave warning that when installing it will overwrite your original AppleRTL8169Ethernet.kext. Note: download this with a browser other than Safari (thanks rocksteady).

25th August 2009
The RealtekR1000.kext works with Snow Leopard with the kernel running in 32-bit mode only.
sk1nhd33t showed it working from either /Extra or /S/L/E, and I posted how I used this to get it working on my system.