Getting there
Both routes start from the A83, east of Inverary. A large car-park is provided for parking at the head of Glen Fyne. Parking at the head of Glen Shira is obvious, although you could try and drive up the glen for 6km where there is parking for 2 or 3 cars.

Ben Bhuidhe via Glen Shira
My prefered choice ! Just north-east of Inverary, a road heads up Glen Shira from the head of Loch Shira. It is possible to drive up this, but this is discouraged by no-entry signs at the glen entrance - so if you're stopped driving up here, don't tell the landowner I told you to do so ! Head up the glen for 6km, past the firing ranges and farms to where a gate blocks access to the forestry land. There is room to park 2 or 3 cars. Beyond the gate, cycle for another 3km up a tarmac'd road to a bridge over the Brannie Burn and leave your bike here. Cross the bridge, then enter the forest directly ahead. There is no escaping the initial thick forest and undergrowth, but follow the burn and a fire-break opens the forest up. Up by the burn and fire-break to open hillside and note the terrain and position of the fire-break in relation to the rest of the forest for the descent later. Turn west, and ascend, occasionally steep, grass covered ground. Pass under a line of wooden pylons, then over a fence-line and start to pick up signs of a faint path. The path becomes more distinct as Tom a'Phiobaire is reached, from where it's a pleasant, if long, walk following the path over several minor tops to finally attain Beinn Buidhe's main summit. The trig-point has long been broken from its base and there isn't much in the way of shelter on windy, wet days. On fine days the views are superb though.

Return
You could just return the way you came up. Alternatively, particularly on days when wind and rain are blowing from the west (ie most days), you could try a quick exit down to Brannie Burn. To do this, from the summit, initially head east along the obvious worn path for a few metres, then turn south. Drop down 100m or so on very steep, grassy ground, then as the ground flattens turn south-west and pick up, and follow one of the Brannie Burn's sources. The ground is easy under foot and once the forest is reached a faint path can be picked up to follow to a track that continues back to the bridge over the Brannie Burn. The freewheel downhill makes the effort required for the uphill cycle worthwhile.