The complication is that 10 August is a Sunday, so there is no direct Ardrishaig to Oban via Kilmartin bus as there would be on a weekday.
On a Sunday all but one ferry runs from Port Askaig on the other side of the island, and the otherwise good island bus service doesn't run on the Sabbath.
So it is the 1245 ferry from Port Ellen, arrive Kennacraig at 1455.
The #926 bus leaves Kennacraig at 1540. The most obvious interchange for Oban is at Tarbet (Loch Lomond) arrive at 1753 on the A83 (west) side of the hotel. Leave on the A82 (east side of the hotel) at 1912 on the #914 headed for Fort William, as far as Tyndrum where there is a booked 5 minute connection into the #978 bus from Edinburgh, arrive at Oban at 2102.
Or from the A83 side of the hotel the #976 leaves also at 1912 direct for Oban arriving at 2107.
If taking that bus you could alternatively have longer waits at Arrochar or Inveraray.
If you got a taxi to Port Askaig you could take the 0945 ferry to Kennacraig, arrive 1150, for the 1235 #926 arrive Tarbet (A83) at 1448, depart from Tarbet (A83) at 1538 arrive Oban at 1733. As above Arrochar or Inveraray are alternative interchange points.
If you travelled next day, Monday, there is-
Port Ellen depart 0700, Kennacraig arrive 0920, #926 depart 0930 Lochgilphead arrive 1008, depart 1015 on the #23, arrive Oban 1142.
and PE depart 0945, Kennacraig arrive 1155, depart 1235, Lochgilphead arrive 1314, depart on the #423 at 1320, arrive Oban at 1445