Hello,
Considering your low budget for the project I would be more like an assistant for you. :)
It is not hard to connect an Arduino to an accelerometer and read the values. But to send it over Wifi or GSM data network, it would be much easier if you use a Raspberry PI board since there are multiple sources and examples on hot to connect usb GSM stick or Wifi stick to it.
I would use Arduino mini pro + any accelerometer that fits in the budget + RPI to send messages. RPI cand also be used for audio-video communication with the person on the bike, or for video assesment of the situation.
Looking forward to share ideas on the project,
gus