Here's two commonly available design of GPS modules that I've been happily using. These are both low cost.
module with onboard patch antenna and USB connection
module with external patch antenna
The first has an onboard patch antenna. That's safe and secure. The second has an external patch antenna that connects via a tiny uFL connector. The external antenna has to be treated with care as they are easily damaged physically or electrically. I've destroyed several.
The first has a SMA connector (the large brass screwed receptacle) for an external antenna if the onboard antenna isn't performing. On the bike, I'd imagine an external antenna would be an inconvenience. Some are supplied with the connector loose, not soldered in. That would be best as you can solder it in only if the onboard antenna underperforms (which is unlikely).
The first also has a micro USB connection. This is very handy as you can feed the raw GPS output direct to a PC and view it on U-center without any Arduino or custom programming. I think it is essential to be able to readily view the raw GPS output. With the second module you need to feed the raw output thru a TTL/USB converter or an Arduino. That's not hard, just not as convenient as the USB connection.