Q:

Who should pay my travel expenses? I'm a 1099 contractor going on a trip for my client

I'm a 1099 contractor to a full-time client in another state. They need me to meet with one of their customers (in another state) in order to try and drum up more work but they are requiring that I pay for my flight, hotel, food, etc... Is this normal? Or should they pay because I'm going on their behalf to drum up more work?
My client said.... 

You should bill us what you expect our client to pay; We can not pay for any expenses or charges from a vendor (you) which cannot be billed to our client.  All ‘internal’ non-billable hours become a cost of doing business.  So I’d pay my own way for any of my own expenses or those of my employees.  As a fellow business owner, I am your customer so the burden of running your own business and all of the costs associated with that are your burden and not mine. I can’t reimburse or pay for a rental car, hotel, food, snacks, entertainment or other on your behalf.

I'm thinking that he's asking me to go represent his company, so he should reimburse me for travel. Is he off-base or am I? Am I expecting too much?

A:

I'm not sure I understand the confusion. If he won't reimburse your travel then you simply charge him for it. This is why you should have various rates based on the work clients expect from you. If you bill X$ an hour for the work you currently do for this client remotely, then you simply bill X+Y$ an hour where you calculate Y based on your expected costs with a generous surcharge for the time you lose while travelling and the general inconvenience. This is standard practice so you shouldn't get any push-back when you quote a different rate for this kind of work, but your client's response isn't the most reasonable so who knows. Regardless, this is what you say:

I'm happy to take on this work but if you don't want the hassle of handling my expenses on this trip I'll of course have to adjust my rate. I charge a flat fee of X$ for all out-of-state work and a per diem of Y$. If that's okay with you I can draw up a quick contract and send it to you by the afternoon?

That's just one way to do it. Some contractors simply quote a fixed price for a time-limited gig like this. Some apply a higher hourly rate and those should include some kind of minimum billed hours. If you travel down and a book a hotel for a week but the client changes his mind after day one then you still need to be able to bill him to at least cover your costs. And that's also why you need a contract for these things.
If your client is just getting hung up on semantics and a general lack of understanding of how billing stuff works then there shouldn't be a problem. But the phrase that makes me think your client might be an idiot is "the costs associated with that are your burden and not mine". That's certainly true to some extent but odds are that he's forgetting that as a business owner you also get to dictate the cost of your product and that clients don't get to dictate prices or demand a sale.
If your client is a fool and balks when people have the nerve to ask to be paid for their work then simply repeat the following ad nauseam:

I'm sorry, but if we can't agree on a reasonable price for my services then I'm not able to take this on.

A:

This part:

You should bill us what you expect our client to pay; We can not pay for any expenses or charges from a vendor (you) which cannot be billed to our client

This means that if you go, you accept the risk that the client doesn't pay ANYTHING.  The client might choose another vendor altogether!  Accepting this condition would be very unwise on your part.  Whoever wrote this to you is full of it.
Travel should be prepaid.  You might negotiate a per diem rate, to be prepaid, for your housing and food.  You could base it on the GSA's per diem rate calculator, which is the standard for government employees and contractors who travel on gov't business.
Whatever you do, don't be the guy who forks out big money on travelling and who has to come back home and beg your client to reimburse you.  Please!

