  Building on the work of K. Mann and K. Rafi, we analyze the large scale
geometry of big mapping class groups of surfaces with a unique maximal end. We
obtain a complete characterization of those that are globally CB, which does
not require the tameness condition. We prove that, for surfaces with a unique
maximal end, any locally CB big mapping class group is CB generated, and we
give an explicit criterion for determining which big mapping class groups are
CB generated. Finally, we give an example of a non-tame surface whose mapping
class group is CB generated but is not globally CB.
