I am looking for the rules relating to just opening a Bitcoin Forum account
Briefly there are two types of rules that you should take into consideration in a case like that:
1. Rules of the bitcointalk.org forum. These are listed here, in the starting post of this thread, and their observance is monitored by bitcointalk.org forum moderators. If something isn't mentioned here as prohibited, then it's not forbidden and doesn't imply forum ban or another "administrative" sanction.
2. Rules of particular bounty campaigns. These are listed in threads of specific bounties (or somewhere on their project's sites) and their observance is controlled by project creators and/or bounty managers.
So, regarding the forum account restrictions, we talk about first type. According to p.18 of these rules, on bitcointalk.org you can register (and use) as many accounts as you want:
18. Having multiple accounts and account sales are allowed [...]
(But you'd better not violate the other paragraphs with these accounts if you don't want to capture the attention of forum mods.)
While regarding the "multiple" participation in one bounty campaign, we talk about second type - and plenty of accounts according to these rules indeed is not allowed. But, if you'd break them, you'll be expelled from specific campain only, not from entire forum or whatever else "worldwide".
Though you can also receive the negative trust for this, but that's a social rating and a different story.