Can the application be deployed locally?
By off site I guess you mean that your Bonita application and Database have to remain in the company private network.
A Bonita server can be hosted on your company local infrastructure without any problem. You can find the installation information in the Bonita Documentation (see "Bonita Platform" on this page)
Note that Bonita Studio embed a test environment that includes Tomcat + Bonita web application + h2 database. When you install Bonita on your own server you will need to install an application server, Bonita web application, database with 2 schemas (we recommend to install a database different from the H2). See the documentation mention above for details.
I hope this helps. Delphine