It may be cheaper for both of you to take a highway bus to a between point and meet up there.
Shinkansen from Osaka to Tokyo (or the other way around) is about 14000 for one way. A night bus for the same is around 4000 to 5000, but will take about 8 hours (!!) to get you there.
However, a bus to Nagoya is only 2500 (from Osaka, 2900 from Tokyo) and will get there in about 3 hours. A 5000 or 6000 roundtrip for each of you, and the cost of a hotel where you go.
If I were in your situation, I would be more worried about spending as much time as possible with my boyfriend putting costs second (but still keeping them important).
If you are meeting up at a midpoint, you can keep costs low while still making the whole event a sort of special thing by meeting at various different places and staying at hotels. Like a special vacation each time you meet up.
