You are actually asking about inbound routing if you want to influence routing to your ASes.
The local preference is local to the AS, and it is for outbound routing. What local preference you have in one AS has no effect on the routing in a different AS, whether or not you own both ASes. Other ASes cannot see your local preference. You could try setting a lower MED on the preferred AS, but another AS may ignore that, or you could try prepending to the AS_PATH, or aonther method, but that, too, can be ignored by another AS.
You can try to influence routing in a different AS, but the point of ASes (Autonomous Systems) is that they are actually autonomous; each AS makes its own routing policies and decisions, independent of any other AS. The administrators of an AS are free to follow your hints (MED, AS_PATH prepending, etc.), or ignore them altogether.
Think about it, you would not want someone in a different AS dictating your routing policy in you AS. The same holds true for other ASes; they don't want you dictating routing policy to them.
In practice, you can probably influence other ASes with AS_PATH prepending. Some may pay attention to your MED. The only real way to be sure that your hints are respected is to get a business agreement with the other AS.