Hello there!

I have a problem. I want to be the Redoran Archmaster and Redoran Hortator but Bolvyn Venim won't show up at the Arena in Vivec.
My journal says that I'm to meet him there but he's not there. He stays at the Venim Manor in Ald'ruhn. When I try to talk to him he just says the same thing and forces me to leave the conversation with a 'Goodbye'.

What should I do?

You are going into the pit yes?

Edit: Disregard that i just realised he doesn't go to arena...

Um, has he challenged you?

Are you sure you don't have any issues with mods that might interfere with Bolvyn's appearance in the Arena script? Do you actually go to the pit where the actual battles are (either waistworks -> door to Arena Pit, or either "plaza" level door which takes you to the stands)?

I'm sure some people can give you more specific ways around this. But, if nothing else works, go in front of him in Ald'Ruhn, strip yourself to remove the Goodbye window, and Taunt (/bribe/taunt/bribe/taunt...) him to attack you. It will count even if you kill him there.

It doesn't work that way...
The game says that I have broken the prophecy.
Athyn Sarethi won't give me the Hortator and Archmaster ranks because I killed Bolvyn Venim "dishonorably".

I'll try to fix this glitch with the console by typing in the appropriate journal codes (Journal, B5_VenimHort, 50 and Journal, HR_Archmaster, 100) and then use the 'kill' command on him. I hope this works.

Huh? Dishonorable if you make him attack you first by Taunting? It also reads in http://www.uesp.net/wiki/Morrowind:Duel_with_Bolvyn_Venim that if you have already killed Bolvyn Venim during the Redoran Hortator quest, Sarethi will name you Archmaster when you ask about duties. Don't know if the killing must relate to either of these quests, though... It seems it should, after all. And should therefore happen in the Arena.

On my first try, I taunted him at home and have been named dishonorable.
On my second try, I used the console to get the journal entries and then I wanted to kill Venym but the game still said that I have broken the prophecy.

Man, I shouldn't have timed these 2 quests so that I could complete them at the same time...

You could also go back to a previous save before you talk to Athyn Sarethi about challenging Bolvyn Venim and iirc you must pick the duel topic when you're talking to Bolvyn Venim. If that topic shows up then accept to meet him in Arena and then leave. Once you enter the pit in the Arena he should attack you on sight.

I have a save before I talk to him but Bolvyn simply won't let me choose topics and says that he challenges me to a duel (I also get a journal entry about that).
After that, I went there naked but there was no 'duel' topic. However, I got another journal entry when choosing the 'Redoran Hortator' topic (he still didn't appear in the Arena).

Maybe I'll start a new game and proceed more carefully now.

When you have your first journal update after that he challenge you for a duel just stop and end the conversion with him, because that's all you need to meet him in Arena.

I tried it, too, but it didn't work. He stayed at Venim Manor.

So you didn't try the naked trick yet? At least it removes the red Goodbye. text and you'll be able to select his topics again. Then click duel.

There is no 'duel' topic with Bolvyn, only with Athyn Sarethi. I have tried every possible way to get him to appear at the Arena but still no success.

Is there a topic "Redoran Hortator" or "Yield" in his dialogue?

Yes, both of them are there.
When I click on 'Redoran Hortator', he challenges me to a duel, but he doesn't appear at the Arena (but the journal gets updated).
When I click on 'yield', he says that he'll never yield and that he despises me.