It depends, but I think a good therapist wouldn't get offended. I personally wouldn't go for a therapist that seems stingy, it's a risk.
I also wouldn't go for a therapist that doesn't seem to want to get back to you or doesn't take an interest in your problems.
When I was looking for therapists, my worst experience was with a woman who 'claims' she treated Transexual clients, but hung up when I asked her about her trans* clients, when I managed call her back from a different phone (Since she would no longer answer to mine) I told her, her website said she was LGBT friendly, she ended up being really defensive and agitated. :/
Eventually, I found a guy who was flexible and took an interest in my problems, calling me back a mere few minutes after I called him. We spoke, and he was lenient in price and time, even going as far as to give me a free first session after he heard I came from a really poor family. I was of course suspicious, but he didn't even get offended when I told him I wasn't looking for a 'gate keeper' He is really helpful and we are currently on our second session.
Needless to say, I hope you find a good therapist, most of the time it's worth the hard work it takes to find one. (: