If you can afford it, there is nothing wrong with getting a taxi.
I was very worried about all public transport as an adult, but was an awful driver, skint and while I was happy to walk 10+miles a day, the kids couldn't so I needed to get over it.
Helpful things: does your bus company have an app? I found this helpful, to see all the stops in advance. Could also sort of follow my own bus on the app and see when my stop was nearing. It also had a google maps bit to direct me to and from the bus stop if needed.
Just stick your arm straight out, good and visible, when the bus is about 100 metres away. 150 m if heavy rain/poor visibility. Put your arm back down when they use the indicator.
Not so nice areas mean lots of people use public transport and are used to it. 'Nice' areas are worse for people being funny about seat sharing. Just pick someone ok/not actively scary looking and sit. No need to say anything: I never do and noone ever does when sitting beside me and I get the bus many times a week. If there are no seats available, ask politely to whoever is in the priority seats (might not work. But if you can wait just a short while without too much issue and it would just be standing the whole way as an issue, then a seat will almost certainly become available at some point).
I'm completely fine now with all public transport - just needed to teach myself how, as I'd never had a clue! I'd always been with someone else who knew how it worked, or walked!
I have often been literally puking with nerves over things, but always found it best to make myself do it anyway and prove to myself that I can, so I reckon give it a go! Have a look for an app for the bus and see if you can find a way to make it practical. But, like I said at the start, there's no shame in that taxi either.