Removing Vines - need advice

[Threeponys]

Desperately need some good solid advice on this.

Stopped at a business today to inquire bidding on the lawn maintenance. They are open to proposal but wanted it to include the removal of weeds on the fence. Those "weeds" are blackberry vines! Not talking a small area either. They are ALL over.

Question: What is the best and most feasible method of removing vines like this. While burning them might be suggest, it's not an option. Also, never done this before so how would you price it out? Difficulty? Time? Per sq. foot? Flat rate?

Bid has to be to the manager by Monday so any solid advice will be appreciated.