gibson...

Have you considered being upfront and honest about it? Pick her up from the airport... in conversation bring up the topic... explain to her that you are attracted to her.. and that you "think" that her signals show that she is to... but that you don't want to jump to any conclusions and that you need her input before either 1) making a huge mistake and making yourself look like an ass professionally 2) missing out on something that you would really like to explore...

Just my 2 cents.. but an open honest approach might be exactly what is necessary for this particular situation.

Good Luck