Stopover within airport

We are flying London - Beijing & staying for 3 nights in Beijing (we are applying for a visitors visa for those nights)

We then fly from Beijing to Bali for 9 nights. We will be returning to Beijing to get our return flight to London - we will be in Beijing airport for less than 24 hours on the way home (not leaving the airport). Do we qualify for Direct transit & don't have to apply for anything else? And should we apply for single or double entry on our chinese visitor visa?

Thanks.