Use a zero-ohm SMT resistor for the strap. The cost of the resistor is about as close to nothing as you can get (tenths of a penny, even on Digi-Key) and will be reliable. You call out which version by using a different bill of material (BOM) when you go to build the board.
Using a solder bridge would not be reliable, and will not pass DFM analysis at the manufacturing side. (They actually design their processes to avoid bridging.)
Even worse, you'd have to have different pastemasks which will far outweigh the cost of the resistors. A pastemask costs about $500 for a small board. For that, you can buy about 500,000 resistors.
The very cheapest way of all if you are fortunate enough to have extreme high volumes is to have a different PCB for each variant. You generally don't want to order more boards than you can consume within 3 months or so, as the boards will oxidize if they sit too long and thus have yield problems.
As far as layout concerns, for fullspeed USB you don't have significant SI issues that would be caused by such a jumper. Even USB highspeed would be just fine with the strap in series, though you'd need to pay more attention to stubs.