Q: How do I transfer Books that were purchased on my IPhone on to my Itunes?

You should be able to copy them over via File > Devices > Transfer Purchases - my downloads don't always copy over either when I sync, whether it's because I manually manage all of my content I don't know.

You should be able to go to purchases in iTunes and download it from there. There is also a setting for automatically downloading purchases made on other devices: http://support.apple.com/kb/HT4539