To go until Debre Libanos shouldn't be very difficult even with public transport. First you must decide if you share with about 12 people in a minibus or 40 in a big one. Big ones are said to be more safe but are less often driving. Buses, big and small ones, in direction to Bahir Dar or Debre Markos still starting from Auto Bus Terra. Between 8 to 12 you will certainly catch one. Minibuses you may get even much later. You will reach Debre Libanos after about one and a half hour.
If you going there with public transport and want to visit some sights a night at Ethio-German-Lodge is highly recommended. Even the drab food as well as the usually cold shower can't ruin this magnificent spot. I would recommend to call in advance because after one of the owners passed away I'm not 100% certain about the lodge state.
The waterfalls and the Portuguese Bridge are located close to the lodge and can be reached within 10 minutes walk. In recent years a fee had to be paid because the lodge owner and the local community couldn't agree on any other solution. Since this time some more or less annoying people hanging out at the bridge and will ask for money and write little receipts.
If you are planning to hike until the gorge I would recommend a local guide too. Someone from the lodge would walk with you for a reasonable price. This makes sense by several reasons:
- because of all the previous trouble, people might not help you to find the right way (I never walked it myself and there is no map)
- locals are very creative in making up new fee's you should pay
- annoying kids will follow you the whole time
By the way the area around the monastery isn't also very convenient for extended hiking trips. Many holy places you probably won't be granted to access. A short Trip to the cave of Tekle Haimanot should be possible.