US-Singapore-Beijing-US

Hi- I'm trying to plan a trip to backpack around southeast asia. The flights are about half the price if we fly into Singapore and leave to come back to the US from Beijing, but I'm confused about the visa policy. Is there any way we can avoid paying for and going through the policy of obtaining a visa with the 72 hour rule? We would be flying into Beijing from Bangkok and would just need to stop there to catch our flight back to America. I've read the policies but am still confused about how it all works. Thanks!