Emma Sheppard, who is a GP, stepped up her campaign after her 11-year-old daughter broke both her arms and injured her leg after she tripped and fell on the footbridge one evening in March this year.
The dated bridge is in a state of disrepair with paint peeling off and rust stains.
The surface is also uneven in places and the steps are badly worn down.
Dr Sheppard said: “These steps are treacherous. We are not sure whether she tripped on something but she fell and really hurt herself.
“She was in a lot of pain and had to be rushed to hospital where she required surgery.
“She has endured a slow and painful recovery which took nearly four months - until June this year.”
The Secretary of State for Transport secured funding two years ago for a new footbridge and now Network Rail has committed to a plan to build one with lifts which could be used by disabled people or people with heavy bags or buggies.
They aim to install it by March 2019 but Dr Sheppard would like it to be built sooner.
Until now the only option for people who are unable to use the steps is to walk 1km away to go through two underground tunnels.
Dr Sheppard added: “This isn’t something that people want to do in the dark.
“It’s not satisfactory and doesn’t help to promote train and active travel in East Dunbartonshire as government policy dictates.
“I’d like Network Rail to get this bridge built now.”
A spokesperson for Network Rail said: “We are committed to delivering the new bridge no later than 2019 and are currently finalising designs before entering the planning process to secure permission for the structure. “Once the design and planning phases of the project have progressed we’ll be able to offer more definitive timescales for the work.”