Travel to a client is billed to the client separately via a magical sentence that Thomas taught me: "I will expense travel as per your standard travel policy."
How does that work exactly? I mean, logistically -- if you're coming in from outside, you generally won't know what their standard travel policy is.
Pitch the gig, sign the contract, then you do the boring logistical details. One of them is arranging travel. At my shop that was simple: "How doed $FOO handle business travel? Are you going to book my tickets/hotel or would you prefer to be invoiced for them?" "Great; send me a copy of your travel policy."
I also thought, early in my consulting career, this would be a big deal. It never was. Nobody who can hire 10 programmers is surprised what a trip from Nagoya to SF or NYC or Berlin costs.
What you're doing is putting the client on notice that (a) you're going to have to travel to complete the engagement and (b) they're on the hook for it. From there, things usually proceed as if you were an employee rather than a consultant: you ask them how you should book the travel, and you get it reimbursed later on.
I think you ask. Rephrased, "I expect to be reimbursed for travel, but will try to keep my airfare/hotel/per diem expenses in line with what your employees get. (Hint: provide me a copy of this policy.)"
How does that work exactly? I mean, logistically -- if you're coming in from outside, you generally won't know what their standard travel policy is.