Let's take a quick look at the grammar of [class.mem]:
member-declarator:
declarator virt-specifier-seqopt pure-specifieropt
declarator brace-or-equal-initializeropt
identifieropt attribute-specifier-seqopt : constant-expression
Bit fields are the third option, members with initializer are the second. So you cannot have both.
However, you can initialize named bit fields in constructor initializer lists, just like any other non-static data member. (But you cannot initialize unnamed bit fields, since they are not members.)