If the Camera was on the handlebars it would provide a more steady video. On the downside you will miss what you see as you turn your head. I do NOT view that as much of a problem for most of the time your head will being pointed forward in the first place. On the other hand, if you see something to the side you will get a video of whatever you see if the Camera is on your helmet, but in most cases you can STOP the bike and point the bike and the camera to what you see, if whatever you want a video of remains where it is within sight.
Now, I am ASSUMING this camera was on your helmet, but you do have a video of your arm and thigh in the video. Either you looked down and to the rear with your head, helmet and camera, or the camera became loose and fell down (I suspect the later, but I can not rule out the former). I hope you were NOT hand holding the camera (And if you were B&H has some means o attachment to the handlebars or your helmet).
I go with B&H for they have been in the Camera business for decades (prior to the net, they were Catalog based Camera and Camera accessories provider): Other places on the net provide as good (and at times better) then B&H. Even with B&H you get what you pay for, the more expensive mounts tend to be Aluminum and thus can take some abuse, the cheaper mounts tend to be plastic and thus you need to be careful with them.
http://www.bhphotovideo.com/c/product/924980-REG/fastcap_tech_ibike_mount_bike_mount_for_handlebars.html
http://www.bhphotovideo.com/c/product/848986-REG/FEISOL_bicycle_mount_31_8_BM_318_Bicycle_Mount_31_8mm.html
http://www.bhphotovideo.com/c/product/1061178-REG/shill_slbm_4_aluminum_bike_mount.html
Adapter for the above for a GoPro Mount:
http://www.bhphotovideo.com/c/product/1061165-REG/shill_slba_1_aluminum_bike_mount_adapter.html
If you are using a SMART phone:
http://www.bhphotovideo.com/c/product/917814-REG/iottie_hlbkio101_one_touch_bike_mount.html
http://www.bhphotovideo.com/c/product/1037707-REG/ram_mounts_rap_274_1_un7u_ram_ez_on_off_bicycle_mount.html
B&H also has GOpro Camera mounts:
http://www.bhphotovideo.com/c/product/1061179-REG/shill_slbm_5_bike_mount_with_gopro.html
http://www.bhphotovideo.com/c/product/1118903-REG/bower_xas_abm_xtreme_action_series_aluminum.html
Just a comment that you need to have your camera on a more solid base, the handlebars are the most solid on a bicycle. This is even true if you have a camera with Stabilization, the more stable the base is the better such stabilization works.
The Helmet will provide some stability more then when you hold such a camera in your hands but the handlebars are the best.
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