Can a factless fact table be a bridge table?
Disclaimer, I'm not into DW, so I may have completely misunderstood the question. That said, a factless fact table sounds like an oxymoron, but I googled for it and according to Factless fact table | James Serra's Blog it's an intersection between two or more dimension tables. A bridge table is typically used to implement an n-n relationship:

CREATE TABLE d1
( d1key ... not null primary key
, ... )

CREATE TABLE d2
( d2key ... not null primary key
, ... )

CREATE TABLE f 
( d1key ... not null references d1(d1key)
, d2key ... not null references d2(d2key)
,    primary key (d1key, d2key)
);   


so I don't see any controversy in such table being both a bridge table and a factless fact table.