If you want an unplanned route, heading up Old Port Road / St Lythans Road (with one turn) until you hit Sustrans NCN 88 / 888 to Bridgend doesn't look too crazy and the recently-updated photographs makes me think it might have been signposted recently. I'd still keep a list of place names to pass through, just in case, though.
That would be 4 miles longer than riding the A48. If you're starting from central Cardiff,
http://cycle.st/j56583551 suggests a back road "balanced" route which would add about 2 miles to the A48 route (shown as "fastest"), but yes, it looks as though an audax-style route card would be needed. It's rather irritating such routes aren't signposted.