Examples Of A Solicitation Of Bribery

In a nutshell, it means to basically ask someone to bribe you in exchange for something in their favor.
For example, you are before a judge. The judge tells you, "I'll dismiss the case for $1000."
That is the judge soliciting a bribe.
Or

"If you leave me a $50 with your license, I'll turn the speeding ticket into a warning".

Or

"The Sun, long a source of special pride and attention for Mr. [Rupert] Murdoch, had illegally paid the unidentified officials hundreds of thousands of dollars in exchange for news tips and “salacious gossip."

"Ms. Akers said illegal activities had been rife at the paper.
'There appears to have been a culture at The Sun of illegal payments, and systems have been created to facilitate such payments whilst hiding the identity of the officials receiving the money', she told the Leveson Inquiry on media ethics and practices, led by Lord Justice Leveson.
The payments involved 'frequent and sometimes significant sums of money' to public officials, she said."

Or
CHRIS BRYANT: Do either of your newspapers ever use private detectives, ever bug or pay the police?
REBEKAH BROOKS, Editor, The Sun, 2003-09: We have paid the police for information in the past, and it’s been—
CHRIS BRYANT: Andy Coulson, who was sitting beside her, tried to say, “but only within the law.” And I pointed out that it’s a criminal offense. It’s corrupting police officers, suborning a police officer.
ANDY COULSON, Editor, The News of the World, 2003-07: The same holds for private detectives, for subterfuge, for video bags, whatever you want to talk about.
CHRIS BRYANT: It’s illegal for police officers to receive payments.
ANDY COULSON: No, no, no, without— as I said, within the law.
CHRIS BRYANT: And then the chairman decided to close the meeting, for some bizarre reason. I would much prefer to have been able to carry on.
CHAIRMAN: Thanks very much. We’re both grateful for your evidence.