The BeagleBone was designed to be a hobbyist computer, so there are many ways to get into it (netboot, usb etc) and lots of helpful documentation on the Internet.
While there are some security-through-obscurity things you can do, the feature you are looking for is called "secure boot". Secure boot makes use of cryptographic methods to ensure the machine boots an OS that it is authorized to run. Similar techniques can be applied to protect applications. It's probably not impossible to break into a secure boot machine, but it's certainly harder.
Secure boot is often implemented with a Trusted Platform Module or TPM. While some TI systems-on-a-chips do support secure boot, AM335x support is weak and poorly documented (and it still needs a TPM).
At least one vendor offers a TPM on a BeagleBone cape. The CryptoCape's developer also has a nice explanation of the secure boot process. Another option would be to look into an AM335x-based single-board computer with a TPM.
Bear in mind that secure boot does make development more difficult, as it's easy to mess something up and brick the machine. There are also those who have philosophical objections to trusted computing. While I personally feel the concern about software theft is overrated, there is certainly a need for a trusted execution environment in a wide variety of fields (e.g. life safety systems).