I think this is very old news. If I recall correctly, the suck my dick comment came during a concert in 1987. Here is a complete description from a forum with a poster that knows what he's talking about:
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Alright, here's something special. A lot of fans have heard of the Axl comment about Jon Bon Jovi sucking his dick. However, I don't think a lot of you have ever heard it. A long time ago the entire GnR show was available on the then called easytree.org, and I downloaded it to hear how it exactly went, and now have uploaded the files on my own server to make you able to hear it yourself.

It's being said in the last show of Guns N' Roses supporting Alice Cooper in 1987. First of all the show starts without the "From Hollywood, Guns N' Roses!!!" introduction but just with Axl being in a mood to rant a lot.

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Then the show starts.
1.It's So Easy
2.Mr. Brownstone
3.Move To The City
4. Used To Love Her
5. Sweet Child O' Mine
6. Knockin' On Heaven's Door
7. Welcome To The Jungle
8. Band Introductions

During the band introductions, Axl introduces Slash as "I don't know what's inside this man but it's weird and it's pissed off and it calls itself Slash and is here to talk to you for a minute."

09.Blues Jam

Then Slash starts his bluesjam, something Guns N' Roses did a lot during their shows in the 80's and some shows of the Use Your Illusion tours in 90's. During the bluesjam Axl comes back on stage and starts his rant and says that Bon Jovi can suck his dick.

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and the show goes on with Out Ta Get Me, which I've uploaded as well, because in some way it's related to this entire rant.

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10. Out Ta Get Me
11. Paradise City

As you might hear it wasn't meant as a comment about Bon Jovi the person, or the music, but as a comment about him having nothing to do with it. I've got the full show in FLAC but am unable to share it at the moment, and I don't think many of you are interested in the full show. Enjoy!
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There was also a flap in the press about a year ago about Axl and Jon and that's where the comments came from about Axl doing nothing for the last 12 years. As far as I know - there was no comment from Axl about that.

Kathleen