He insisted he was not a paedophile but was just "bloody angry" at a hate campaign against him and thought "I might as well do it."
Prosecutor Brian Altman QC asked: "This was all about revenge?"
The defendant replied: "Partly."
Mr Altman went on: "So the attempted murder of (the girl) was born out of revenge by virtue of the three years of the hate you and your family suffered?
"You are portraying yourself as a victim. This offence was all about sexual gratification and you are a paedophile?"
Bishop denied it.
Mr Altman continued: "You enjoy controlling children and one aspect of your control of children, particularly girls, is sexual gratification."
Bishop said: "No, not in any way."
The prosecutor asked: "Why did you choose a young girl who was two years younger than the age of the two girls you were accused of murdering?"
Bishop said: "It could have been anyone. Through the psychological trauma of the hate campaign and what everyone else was saying it came out in that behaviour."
The defendant said he assaulted the girl to "belittle and shame her because I was bloody angry at everyone - at her and everyone who had done that to me."
Mr Altman asserted: "This is all rubbish. This is all lies.
"You attacked that young girl because you had a sexual interest in children. It had nothing to do with three years of hate but everything to do with Russell Bishop and your character, didn't it?
"There are very good reasons for what I also suggest are obvious and striking similarities between the two offences because the killer of those two girls in October 1986 was the same person who attacked (the seven-year-old) in 1990. And that man is you.'
Nicola Fellows and Karen Hadaway were sexually assaulted and strangled in Wild Park in Brighton in October 1986.
Bishop denies murdering them.
The timeline of the case, as told to the jury
October 9, 1986: Two nine-year-old girls from Brighton, Nicola Fellows and Karen Hadaway,
October 10, 1986: Girls were found dead in the woods at Wild Park in Brighton.
1987: Russell Bishop, then aged 20, was charged with the murders but was cleared after a trial at Lewes Crown Court.
February 4, 1990: Bishop attacks seven-year-old girl in Brighton.
December 13, 1990: Bishop is convicted over 1990 attack.
October 16, 2018: After Court of Appeal overturn previous not guilty verdicts, Bishop goes back on trial for a second time over the murders.