It doesn't pay particularly handsomely. GABA is probably the biggest eikaiwa of its type, and it pays you (the teacher) in hourly wages.
From here:
Teaching in Japan : Gaba One to One English : Opportunities for Growth
These are for 40minute lessons (but you will need to put in at least 20minutes of lesson preparation so considor them hourly rates). My friend who worked there was not reimbursed for getting to the offices either, so similar to your situation.
Starting teacher: 1500 yen any time
Mid-experience teacher: 1900 yen peak times / 1500 yen off-peak
Top-level: 2200 yen peak times / 1600 yen off peak
One thing to take into account is that that is what YOU are paid at GABA, not what the client is paying. So I would say that being paid any less than 1500 yen by your client is a bit of a rip off as it would cost them 3000 yen + elsewhere.
Most working Japanese taking one-on-one lessons only have a lesson once a week, so she perhaps wont be receptive to your suggestion that she needs to spend more time (and money) with you each week.