I guess you could ask them and see whether that would be acceptable to them, so long as everything was above board, documented and all tax information provided. It's worth remembering that they may wish to do it themselves to ensure that they get the best deal possible, or they might be bringing in several candidates and it's cheaper to have you all travel together, or they may even utilise a 3rd party that books flights etc for them at a preferential rate that you might be unable to get.
At the same time, and you won't really know this until the provide the travel details, they might be rather lavish and spend more money on providing a really relaxing, positive experience for potential candidates which you may miss out on by paying for it yourself.
As for steps I'd speak with HR / recruitment and see what they think, if they're willing and you can get it in writing, then ask for a copy of their expenses procedure. Once you have that in place you can book everything and follow their expenses procedure to get your money back (how will vary between companies - hence the EP).