You can turn off the Forced Withdrawal setting in the Configure Princess Bot dialog. It's a button to the left of the direction dropdown; when clicked it shows a red-ish X next to the text and disables the direction dropdown. This will have Princess keep all units on the board, even when crippled. However, it does tend to play more aggressively when doing this.
You will also need to disable the Auto Flee Board option. Same dialog, just below Forced Withdrawal. This is turned off by default, unless you are launching MegaMek from MekHQ, in which case certain scenario types will enable this and set a direction automatically.
Double blind/sensor contact rules can change this if used. If Princess has no contacts - no visible targets or sensor contacts - then it won't move to seek out targets. There's a few ways of handling that, while limited to 48.0 stable. The first is to do what you've already mentioned, set the Auto Flee direction to the other side of the playing area; but once it makes contact/gets within weapons range, /kick the Princess player then use the Game menu => Replace Player... menu item to change the setting to turn off the Auto Flee setting. Another option is to detach several scouting units into one or more separate players but all on the same team. These can be set to exit the far edge, or they can be set with deployment zones of center or one of the corners or edges closer to the human players deployment zone.