There are tickets for a week/month on the Subway and Tokyo Train system but they are usually only worth the money if you do more than 2-3 Trips a day.
The Suica is a RFID chipped card that you can charge and than you won´t have to worry about fares and tickets. You will just need to recharge it and you can get the deposit back when you return the card.
There are lots of night bus companys doing the trip to Osaka. Here is a little overview of the other routes possible
Highway Bus Routes from Osaka
Here is the page from JR
HIGHWAY BUS TIMETABLE | JR BUS KANTO wich operates buses from and to nearly anywhere in Japan. JR is expensive, so try to find another company if you want it as cheap as possible.
I just checked this company
高速バス/深夜・夜行バスのご予約ならWILLER TRAVEL but it seems that the cheapest JR bus is around the same price, maybe its different for this trip because its a famous destination but i remember going from Yamagata to Tokyo and JR was way more expensive.
There are daybuses but they are usually more expensive and you might get stuck in traffic/only reach the cityoutskirts by this buses.
If you are in Japan during the right time you can get a special ticket that will let you travel 5 days (don´t have to be suggestive) unlimited on normal JR trains (no shinkansen,Sleeper or Limited express). This would cost 2000yen a day and it is possbile to get to Osaka in one day (with good planning). This is the cheapest option other than Hitchhiking but it took me good 11hours to get to Kyoto like that.
Hope i could help