Overnight Buses are considered the most economical because you're essentially saving on one night accommodation and getting from one point to the other.
ANA and JAL have the so-called JAPAN Fare/ Explorer Pass where they have special rated for domestic travel to foreigners who have international inbound and outbound tickets. For our interests, one-way flights to and from Osaka and Tokyo are 7,560 Yen, not including baggage fees above the 20kg free allocation.
But you might consider if booking a multi-city itinerary or opened-jaw would be cheaper.
For example let's get ANA and in my case: Having an open-jaw itinerary (Home > Osaka via connecting flight from Tokyo, then Tokyo > Home) for 400 USD
However, I can get a multi-city itinerary ( Home > Osaka via connecting flight from Tokyo; then a domestic flight from Osaka to Tokyo, then finish off with a Tokyo > Home) booking for 420 USD. That's only a 20 dollar difference. Your mileage may vary, so to speak.
One way Tokyo <> Osaka Shinkansen tickets cost 13,500 Yen.
IF riding the bullet train is on your bucket list, go ahead.
IF you're doing a round-trip and/or have some sightseeing checklist in the other prefectures (pay respects in Hiroshima or make a pilgrimage to Sapporo) you might consider a 7-Day JR Pass, which costs 29,110 Yen. It pays off with just a Osaka<>Tokyo round trip but the more you use the JR lines the better.