First, this is my opinion, not facts.
Add to the conversation, but let's not argue about things. This is meant to focus people into achieving a goal: a line of stations between the Bubble and Colonia.
So my first thought is: We'd have to get organised. This means communicating as a group. You might say that won't happen, too many will be trying to achieve things for themselves and not for a group trying to achieve a goal, but there have been many such groups already. The successful ones got organised.
This means: People would have to put the needs of the goal above their wants and desires. I know already I will want a system myself, and I am sure I will get there, but if I were part of a group whose goal was a line of stations between the Bubble and Colonia, I'd have to accept and agree to put the needs of the goal above my wants. Not in a strict sense, but if you want to help achieve this goal, you can't have a conflict of interest. For example, there would have to be a number of systems colonised, and if you're gathering materials to colonise your own system, you can't easily gather materials to contribute to colonising the next system in the line.
People would have to be willing to help those helping in the goal. There should be a benefit to helping, whether that's getting a commander back on their feet if they crash and respawn or if after helping others or the goal, decide they want a system. It should be ok to help them in return for them helping achieve the goal. Community spirit is important, and helping others needs to be a part of it.
Everyone helping gets a system in the line between the bubble and Colonia. If you're helping, and others are also helping, we'd need people to claim systems. If you haven't yet claimed a system, maybe there's an organised queue or something, when it's your turn (or something), you claim the next system, and this group trying to colonise a line to Colonia, then all help you get your system colonised and built. Then when it's done, you carry on helping someone else claim and colonise the next system. Ideally, every person in the group helping, has at least one system claimed in the line. This is part of all of us helping each other.
It should be ok if people want to or need to drop out of helping. I think this speaks for itself. It's basically don't judge others and don't think badly about them if they decide that's all they want to do. Thank them for their help, they are still a part of the Elite community and awesome in their own way.
And lastly I think, arguments should be avoided or quickly resolved. In-fighting won't help and would be counter-productive.
These are just my thoughts on what it would take to colonise a line to Colonia. I am sure everyone has ideas to achieve this.