My advise comes from my own experience.
Colleague behaves in a very insular way, does not share ways of working and ends up creating a situation where I often have to try and 'figure out how current processes work'
Although it's not clear from your question what you mean by insular, it's very important to build up a good relationship. If the two of you don't get along, it will make things worse. Try to show some interest like "you did that very well!". Then ask her if she can show you how she did it. Although this might seem a bit anoying, it is not. Try to ask her how things needs to be done, don't expect her to come to you. Thank her afterwards.
I end up making a mistake from assuming it is supposed to work in a certain way leading to her blaming me for messing up.
It is very important to understand the true meaning of someones statements. Maybe it feels to you that she is blaming you, but maybe she doesn't mean it that way. She is even more responsible for your actions at this moment, try to tell her that nobody told you how to do it and that you don't want to bother anyone, so you tried to solve the problem instead of doing nothing. Ask her how she thinks you can do it better. This way you are showing her that you take her serious and respect her advice.
Don't be afraid to ask or do something wrong. You are there to learn. From my own experience, if something doesnt work out the way I hoped it would be, I just see it as a new life experience. These kind of situations are not unique, so it's better to learn from it.