宿泊予定のホテルに「空港までの送迎手配をお願します」って英語でなんて言うの？

By adding "if so" you are able to ask two questions at once while keeping in mind the potential answer to the first question. This is both polite and direct. I hope that this helps. :)

An "airport shuttle" or "shuttle service" are terms used to describe arranged trips between the airport and the hotel, airbnb, etc. where one is staying. Such trips can either be complimentary (free) or come at a cost. These expressions are used industry wide and are readily understood. And it doesn't matter whether or not one is coming or going. "How much is it" or "how much will it cost" are common phrases used to inquire about an item or service's price. Make sure not to confuse between the prepositions "to" and "from". "From" refers to the place you will be leaving and "to" is always where you intend to go. E.g., The airport shuttle will pick me up from the Haneda Airport and take me to the hotel. Do you know how much it will cost?

"Does the hotel offer transport..." The verb "to offer" in this case is synonymous with the verb "to provide". Since hotels provide various services, it can be said that they offer various services. So, it is reasonable to ask if they "offer transport from the airport". By asking this, you are asking if they provide transport. "How much do you charge?"="What is the price?"="How much does it cost?" In case that the hotel does offer transport, these are three expressions you could use to ask what the cost of transport is. "Arrange transport"/"arranged transport" is another way of saying organized transport. This implies that the hotel provides organized transport.

"Do you have an airport shuttle?" - A 'shuttle' is any form of transport that goes regularly from one place to another and is commonly used when referring to a service a hotel offers as an 'airport shuttle'. "Is it complimentary and if not, what is the cost?" - Often airport shuttles are complimentary if the hotel is close to the airport. The word 'complimentary' means without cost. "What is the best way for me to get to you from the airport? How much does it cost?" - This is the most straightforward and general way you can ask a person for their recommendation of transport along with what the cost of it will be.

"Is it possible to book a transfer to the airport, and if so, about how much would that cost?" Here is another example to ask if the hotel provides transportation and how much it will cost to do so. With the word "possible" you are asking if you are able to schedule the appropriate ride that you need for the airport.