Just my opinion, but I would find it easier to speak to them on the phone before confirming the booking a). as part of the vetting, i.e. do they sound OK, and b). to check what they're looking for etc.
I don't think an auto-response would come across as rude if it was worded appropriately, but when I get a general email I say something like, "Thanks for your message - give me a call when you know your schedule and are ready to organise a booking."
I never confirm a booking without a phone call.
I currently have a day job and take bookings in the evenings and on weekends, I just think it'd be a little sporadic trying to answer and return phone calls during the day.
I personally have never had any issues with my screening process.
My auto reply definetly sorts the wheat from the chaff it answers all the usual questions of availbility post code whether theres parking etc and directs them back to my profile for answers to the other stuff.
I have quite a lengthy paragraph on my profile explaining the info I'll need from them to arrange a booking but I always get the availability or nearest station question. It seems I'll end up with a lengthy autoresponse too!
I have an auto response like Miss Delaney and it definitely sorts out the TWs.
I am very specific in mine and it works. Genuine clients are not put off as it is worded well. Likewise, I have a statement at the end addressed specifically to the bottom feeders so that when they text me offers for my services or ask for services I don't offer they know they have just wasted THEIR time, not mine. 
I think mine would be somewhat polite and friendly, it's just generally an autoresponse makes some people feel put out because "other ladies bother" to respond to each and every message.
I used to use one of these, these days I find just laying out the things I require on my profile works better. I also stipulate not to contact me unless you have those details, I can then refer back. Sometimes I just reply straight yes, or no (with thank you for your email, signed off with my name) and wait for them to provide the info whilst getting on with my day.
Currently on my profile I have a section (with header, bold and italic text for effect) letting potential clients know that I need their name, contact details and when they'd like to book in their initial email so that I can check my availability. I also have a little paragraph saying that new clients will need to be screened, how I do that and if they're unhappy to do it I can't provide a service.
I'm finding it hard to be direct as well as light and friendly!
Thanks for all your comments ladies, I think an autoresponse is the way for me to go.