If you've already reported this to the police and they came in and took a statement and you have also alerted your home insurance carrier, if that's applicable, then you've done what's most important, and the rest is going to depend upon the police.
If you gave them enough information for them to link this to your ex, they can get a search warrant and, obviously, if any of your property is there, they can make an arrest. The problem is that while you may very well be correct about who did this to you, if it's only a good hunch it will not be enough evidence for the police to be able to convince a judge to let them search.
If they can get a warrant, however, and they know where to find her, this shouldn't require a very lengthy investigation
. You were probably given the name of a detective who would be assigned to your case. You ought to call him and find out the status of the investigation. And obviously, if you get any additional information that points to your ex, you should provide that to the police as well.
If you feel you are getting a runaround from the police and nothing is really getting done, you can go to the prosecutor's office and see if you can interest the prosecutor in your case. This is a burglary, so it's worth a try, and the prosecutor can order the police to investigate more aggressively, which should be helpful.
From there, unless you want to hire a private detective to see if he can find you a hard evidentiary link between this burglary and your ex, you are going to have to wait for the police results. But call them and remind them every now and again so that you can get yourself an update. YOu're a victim of a serious crime, and there's no reason you have to be shy about it.