If you only run one Tumblr account with ASB Tumblr Bot, you do not need to buy a private proxy. You will need to buy a private proxy when using two or more Tumblr accounts. ASB does not work with public proxies.
ASB Tumblr Bot runs on an emulated platform similar to the Tumblr apps used for Android. Therefore, your Tumblr account(s) will be completely safe. The accounts can only be locked if you do not abide by the rules on Tumblr.