Black Britons can't bring centuries of white guilt to bear with the devastating impact that African-Americans have done for two generations. For the most part, we have been here for less than 60 years.
'(F)or the most part' above means mainly, generally.
There's also a part of me that feels indignant on behalf of my Caribbean slave ancestors.
I have mixed feelings. Partly I (a metaphoric part of me) feel indignant.
BTW, what does 'bring to bear' mean in the context?