The high-profile politician, speaking in the wake of the death of fellow MP Sir David Amess, suggested elected politicians may need to return to dealing with constituents either online or over the phone as they did at the start of the coronavirus pandemic.
Sir David was killed while meeting constituents in Essex on Friday, with Ms Cherry saying there could now be a need to “consider whether MPs can continue to meet total strangers at vulnerable locations such as libraries and church halls”.
In July a court ordered Grant Karte not to contact Ms Cherry for five years after he sent threatening messages to her on Twitter.
At the time Sheriff Alistair Noble said that the threat from Karte “carried implications of violence and one interpretation of what was said was sexual violence”.
Ms Cherry wrote today of other threats she had received, saying: “On one occasion I required a police escort at my constituency surgery because of a death threat considered credible.
“On another occasion a constituent behaved in such a menacing and threatening manner I and my office manager were in fear of our lives.
“We were so terrified that after he left we pushed all the furniture against the door of the room in the suburban library where my surgery was being held while we waited for the police to arrive.”
And she said that these “unrelenting attacks do take their toll”.
The Edinburgh South West MP added: “Recently I contemplated leaving elected politics due to the level of abuse and threats but I’ve decided to stay and fight my corner.”
But she insisted: “We must not let the bullies win.
“Our democracy is at stake.”
Sir David’s death comes after Labour MP Jo Cox was killed in 2016 while on her way to a constituency surgery.
“Two murders in the space of just over five years is not only unacceptable, it’s terrifying,” Ms Cherry said.
She added: “One of the good things about Scottish and British politics is the accessibility of our parliamentarians to their constituents.
“It would be awful to lose this but we do need to consider whether MPs can continue to meet total strangers at vulnerable locations such as libraries and church halls.
“During the height of the pandemic we took our surgeries online or by phone.
“We may need to return to doing this while Parliament and the police look at what should happen in the long term.”
Ms Cherry also said there needed to be a change in the “public discourse”, stating: “We need to take all threats against people in public life seriously, even if made against those with whom we disagree.”
Here she urged: “Politicians in particular must show leadership and avoid the demonising and targeting of other politicians.”