What process do flight attendants and pilots follow to bid for routes?
It totally depends on the airline and is different from one airline to another. There is no standard way of distributing schedules. Some of the ways that I have personally experienced or have seen it:


Bids by seniority: The crew will bid for flights/rosters based on their seniority. Juniors will cry rivers. 
Fair share: The crew will get turns, if you take a specific flight this month, next month you will not get it until everyone else gets it, and so on. Seniors hate this, they will feel unjust and keep complaining that how come a junior took their righteous flights and off. 
A combination of fair share and seniority: Crew will get points, the amount of points they get depends on their seniority and other factors, then they use these points to bid for flights or days-off. For example, you can bid 100 points on getting days-off during Christmas and another 100 on getting a Paris flight during new year's eve, while someone else will throw his/her 200 points on the days-off only, and so on. 


Almost all systems have some sort of giving the crew the option to at least bid for their desired off. Some other airlines just distribute the rosters randomly and then the crew will trade duties to get their desired flights and days-off, some have a system depends on the crew performance, there isn't really a standard way. 

The ultimate target for airlines is to distribute flying hours among the crew equally, to avoid unnecessarily over-time costs and crew legality issues.