Ciara
You will get a lot of looks and stares which are uncomfortable, but so would a white man. Africans are very supportive of someone in need and there would be hell to pay for anyone harming or stealing from anyone, let alone a tourist and if you make a scene then people will always come to your aid.
It might make sense to stay a night or two in Kampala Backpackers or Red Chili in Kampala if you are concerned and see if anyone wants to ride the same route as you. I stayed at Kampala Backpackers for three days and very soon had a gang of six heading out to Fort Portal
Alone at night might be a bit sketch, the intercontinental buses like Kampala to Nairobi and probably the long distance companies inside Uganda like Jaguar should be fine as they are well known and well used with seats booked and named so it would be hard for anyone to get away with anything on them. it would also be hard to avoid travel at night due to the distances (a bus will either leave first thing in the morning or around 8pm - i always opted for the first thing in the morning but you might still arrive at your destination at gone 10pm). I would steer clear of minibuses and buses with no clear name or company attached to them after dark
I met more girls traveling alone in Uganda than guys and all had great experiences, just use common sense and treat it like a new European country you have never been to. Safety first!