How to organize a Joint Collaboration Plan and Fees
In theoretical computer science (which I work in), the most direct answer is "What bills?"

For remote/electronic collaboration, there really are no significant costs.  Each collaborator uses their own computer equipment and their own internet access.  They install LaTeX and Skype and svn themselves.  They typeset and illustrate their own papers.  They each buy their own espresso at their own favorite coffee house.  There are no fees associated with submitting or publishing papers.

On the other hand, if you actually want to travel, either to give a conference talk or to work in the same physical location as someone else, there are real costs.  For conferences, usually each person (or their grant, or their advisor, or their department) pays for their own travel, lodging, and registration fees.  For collaborative travel, every trip is different, but some common protocols include:


The visitor (or their advisor/grant/department) pays all costs for their visit.
The visitor (or their advisor/grant/department) pays for travel, and the host (or their advisor/grant/department) pays for lodging. 
The host (or their advisor/grant/department) pays all costs for the visit.


I have used all four of these arrangements (and various ad hoc mixtures), as visitor, as visitor's advisor, and as host.  For some visits, I've had small joint grants specifically for collaborative travel; in others, I've used travel money from a larger grant; in others, I've paid (either for myself or for my guest) out of my own pocket.

In short, F'X is exactly right: It depends.  Obviously.