By all Biblical accounts, Jesus wasn't buried by the Romans. Joseph of Arimathea asked permission from Pontius Pilate to do remove Jesus' body from the cross for burial. This permission was granted, and Joseph and Nicodemus removed Jesus from the cross, wrapped him in a cloth, and entombed him. Even the Romans were capable of respect for the dead.

There are various conflicting theories on what happened to his body (including burial by the Romans as a criminal), but debates about the historicity of the Bible are a whole other can of worms. Some historians argue that the Romans would never release his body, but support for claims either way is minimal. There's just not all that much information about these events outside of what the Bible says.

The bottom line is that nobody actually know what happened to Jesus' body.