DS(20) has issues like this. He has dyslexia and social anxiety. He also had a terrible experience some years ago where he was put on a train, alone, at age 13 with all his belongings and sent 250 miles to live with an uncle because his birth mum didn't want him any more. He had no phone, no itinerary, nothing but his ticket and his uncle's number written on a piece of paper. Nobody to meet him at other end. He had to knock on a stranger's door and ask to use their phone. His uncle didn't even know he was coming. 
Unsurprisingly, it's given him some phobias around travelling alone. After he came to live with me at 15, we came up with some strategies to help him. When he had to make a new journey on the bus, I would go with him and do a "trial run" so he knew what landmarks to look out for to get off, etc. We would write down which bus number he could get. I got him a smartphone so he could use Google maps which is really helpful for using their public transport directions thing. Also if he did get lost he knew he could just open Maps and tell me what road he was on, and I could direct him back onto the right route.
It was always cheaper for him to get a day ticket, so no worries about fare costs as they were always the same. This also meant he could use his ticket on a different bus number if necessary.
He now lives away from home and still has a problem catching buses if he hasn't gone on that route before. However he does do it as long as he can sort of "dry run" it with me before. We will get on the phone and I'll look up the bus stop for him on Google maps and tell him "It's outside the Co-op" or whatever.
What I would probably do is a week or so of catching the bus with her. Firstly you going on and getting both your tickets. Then going to both of you getting your tickets separately. Then finally to her getting on before you and sorting herself out, then you getting on after and sitting separately. (If you're very rural and there isn't anyone else at the stop then there might only be two stages to this!)
When she says she "feels lonely" I wonder if she means that if she starts to feel anxious there is nobody to reassure her? If that's the case then some self-soothing techniques could help massively. CAMHS can help with this. I would push to get someone to work one on one with her because this is going to significantly impact her day to day life and restrict her activities if she can't get a handle on it.
You didn't mention whether she has problems coming home. Is she the same way or is she less anxious? Is the underlying fear that of being late and getting in trouble?
Good luck 