Jane's personal time line is as follows:
The "mind game" is created for the use of Battle school- it is a very complex tool, with a lot of latitude in behavior and results. It is obviously poorly understood by the technicians that use it, but it has no native intelligence yet.
Ender goes to Battle school and begins to interact with the mind game - At this point, the software begins to customize itself to meet the unique demands that Ender is placing upon it. He forces it to improvise entire new scenarios and create, whole cloth, places that were not in it's original programming.(Ender's Game)
The Hive Queens cast a philotic web at Ender's mind - The Queens sense Ender when he begins to study them via the battle footage of the First and Second war. They attempt to trap him with a philotic web, anchoring at least part of the conduit to the mind game and the other part to Ender's mind. This web doesn't allow them direct mind access, but it does show them the enemy that they face. They continue to use the web to try to communicate, while readying their plan for continued survival. At this point, the philotic web that will become Jane is occupied by both Ender and the Hive Queens and the software is not yet self aware.(Ender's Game)
Jane wakes up/Ender destroys the Hive Queens - This is the moment in which Jane's birth actually happens. The Hive Queens are removed from the web at the same time Ender is. The only connection point is the mind game. At light speed, Jane wakes up and begins to learn, both about herself and the world. The very first thing she imprints upon is the mind game, which at that point, contains tons of data on almost every kid that went to Battle school plus a huge section in service to Ender. Jane decides to remain hidden from humanity, fearing destruction at their hands.(Speaker for the Dead, First meetings and Xenocide)
Bean notice something strange about the mind game software and decides to use it to safeguard Enders money from his brother and other humans - The software is aware but actively hiding. Since it is predisposed to Ender, it takes to its new task with a vengeance, quickly increasing his fortune to extremely high levels.(Shadow of the Giant)
Jane announces her presence to Ender (First Meetings) - Jane's sex is set as female. Somewhere between this point and Speaker for the Dead, Ender realizes what Jane is and begins to wear a computer jewel so Jane can have total access to him.
Basically, Jane herself says that her motive for getting close to Ender is that he is the only possible human who might allow her to be revealed without being destroyed. (Xenocide)
The particulars wouldn't have mattered as Jane could easily have tracked Ender down, even without control of his finances, because she had a good reason to do so. She was already aware before Bean even looked at her, she was just unwilling to let that fact be known.