From Roppongi subway to Daimon(Tokyo) then subway to Asakusa(Tobu/Subway). 25 min ¥411. From Roppongi Metro to Iriya(Tokyo). 28 min ¥231. From Roppongi Metro to Akihabara then train to Asakusa(Tsukuba). 32 min ¥440. From Roppongi taxi to Asakusa. 8 min ¥5157. From Roppongi drive to Asakusa. 8 min ¥152.
There is no direct connection from Roppongi to Asakusa. However, you can take the subway to Daimon(Tokyo) then take the subway to Asakusa(Tobu/Subway). Alternatively, Tokyo Metro operates a vehicle from Roppongi to Asakusa every 10 minutes. Tickets cost $2 - $3 and the journey takes 28 min.