The 58-year-old academic told BBC Radio Five Live: "There's something very strangely and awkwardly insidious about it.
"It is scary and it has got to stop. I didn't actually intellectually feel that I was in danger but I thought I was being harassed, and I thought I was being harassed in a particularly unpleasant way."
Hadley Freeman, a Guardian columnist, Grace Dent, an Independent columnist, and Catherine Mayer, the Europe editor of Time magazine, plus a number of other women, have previously said they have been the subject of bomb threats on Twitter, while two women have received threats of rape.
The Telegraph's Women's Editor Emma Barnett also received the threat.
Others argue that such a silence will hand a victory to the ?trolls? and misogynists behind the threats.
Ms Beard tweeted today: "Planned to be off twitter, but I've had more threats this morning (rape and worse). It IS still going on. Tried to report to Twitter, failed."
She added shortly afterwards: "Have reported to police. Failed to make the Twitter report form submit!"
The anonymous Twitter accounts from which the bomb threats originated were suspended, although screen grabs were widely circulated online.
Scotland Yard said an investigation into eight allegations had been launched.
Tony Wang, Twitter UK general manager, posted a series of tweets yesterday saying abuse was "simply not acceptable".
His messages came after the website clarified its rules on abusive behaviour amid a growing backlash over a series of attacks.
Mr Wang wrote: "I personally apologise to the women who have experienced abuse on Twitter and for what they have gone through.
"The abuse they've received is simply not acceptable. It's not acceptable in the real world, and it's not acceptable on Twitter.
"There is more we can and will be doing to protect our users against abuse. That is our commitment."
The company has updated its rules to make it clear that abuse will not be tolerated and has put extra staff in place to handle reports of abuse, it said.
Scotland Yard said its e-crime unit was investigating allegations by eight people of abuse on the microblogging site.
An online petition calling for Twitter to add a "report abuse" button to tweets has already attracted more than 124,000 signatures.
An "in-tweet" report button has been added so people can report abusive behaviour directly from a tweet, Twitter said.
In separate incidents, Labour MP Stella Creasy and Caroline Criado-Perez, a campaigner who successfully fought for a woman's face to appear on ?10 banknotes, were threatened on Twitter with rape.
Two arrests have already been made in relation to those threats.
A Metropolitan Police spokesman said: "Detectives from the Specialist Organised & Economic Crime Command have taken responsibility for the investigations into a number of allegations recently made to the MPS (Metropolitan Police Service) relating to allegations of malicious communication made on the social networking site Twitter.
"The Police Central e-Crime Unit, who hold the police national cyber crime remit, is now investigating allegations made by eight people that they have been subject to harassment, malicious communication or bomb threats."
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