I think wordlength (as a single word, or two words separated by a hyphen or a space) is a bit "geeky" these days. Non-specialists invariably refer to 32- or 64-bit systems, and programmers usually refer to 4- or 8-byte [native] integer size where the distinction is relevant. But if they were happy with the term itself, I doubt anyone would quibble over which written form you used.
But bitbreadth is really a non-starter. That single instance in Google Books is effectively an accidental collocation, and most instances of the two word forms are actually references to the width of a drill bit. Bit width is more common, but doesn't really suit OP's intended context.
Bear in mind that word length normally means length of a "word" in computing contexts, which can meaningfully vary. But extrapolation to length of a [computer] bit is meaningless - what OP means is width/length of [something] as measured in [computer] bits.
Even geeks don't normally say things like "This compiler supports integers of bitwidth X" (but if they did, they'd use bitwidth, not bitbreadth). In practice, they usually follow the same style as non-specialists, and speak of 32- or 64-bit integers, for example.