R, 141 bytes

function(x)intToUtf8(matrix(match(el(strsplit(gsub("D","",x),"B"))[-1],paste0(rep(c("",y<-c("I","A","O")),e=4),c(y,"U")))-1,,2,T)%*%16^(1:0))

Try it online!

Using some modular magic is likely to be shorter, but I'm pretty happy with this as a naive first pass.

R, 141 135 bytes

function(x,y="I":"A":"O")intToUtf8(matrix(match(el(strsplit(gsub("D","",x),"B"))[-1],paste0(rep("":y,e=4),y:"U"))-1,,2,T)%*%16:1)
":"=c

Try it online!

Thanks to JayCe for saving 6 bytes!

Using some modular magic is likely to be shorter, but I'm pretty happy with this as a naive first pass.