The essence of the entrapment defense is that government pushed someone to commit a crime who was not otherwise predisposed to commit that crime. Thus, it is not entrapment for the police to use an undercover agent to merely afford the opportunity for a person to act who is predisposed to commit the crime. The classic example is a cop on a street corner who says to you “hey buddy, you want to buy some crack?” The cop is in that instance simply opening the door to you; if you are already in the market to buy drugs, i.e. already predisposed to buy crack, you might bite and buy the crack. If you aren’t already interested, you’ll say “no thanks” and keep walking. Thus, that situation is not entrapment. The government is not pushing you to commit a crime where you are not initially disposed to do it. It is just providing an opportunity. As the Supreme Court explained:
Sorrells and Sherman both recognize ‘that the fact that officers or employees of the Government merely afford opportunities or facilities for the commission of the offense does not defeat the prosecution,’ 287 U.S., at 441, 53 S.Ct., at 212, 356 U.S., at 372, 78 S.Ct., at 820. Nor will the mere fact of deceit defeat a prosecution, see e.g., Lewis v. United States, 385 U.S. 206, 208—209, 87 S.Ct. 424, 425—427, 17 L.Ed.2d 312 (1966), for there are circumstances when the use of deceit is the only practicable law enforcement technique available. It is only when the Government's deception actually implants the criminal design in the mind of the defendant that the defense of entrapment comes into play.
United States v. Russell, 411 U.S. 423, 435–36, 93 S. Ct. 1637, 1644–45, 36 L. Ed. 2d 366 (1973).
Contrast that with a case in which the Supreme found there was potential entrapment. In that case, the defendant was convicted of buying child porn. But unlike the street drug dealer example above, the cops didn't just approach him one day, offer to sell child porn, and the guy bit on the opportunity and bought the stuff. Instead, the government did much more than that:
Had the agents in this case simply offered petitioner the opportunity to order child pornography through the mails, and petitioner-who must be presumed to know the law-had promptly availed himself of this criminal opportunity, it is unlikely that his entrapment defense would have warranted a jury instruction. Mathews v. United States, 485 U.S. 58, 66, 108 S.Ct. 883, 886, 99 L.Ed.2d 54 (1988).
But that is not what happened here. By the time petitioner finally placed his order, he had already been the target of 26 months of repeated mailings and communications from Government agents and fictitious organizations. Therefore, although he had become predisposed to break the law by May 1987, it is our view that the Government did not prove that this predisposition was independent and not the product of the attention that the Government had directed at petitioner since January 1985. Sorrells, supra, 287 U.S., at 442, 53 S.Ct., at 213; Sherman, 356 U.S., at 372, 78 S.Ct., at 820.
Jacobson v. United States, 503 U.S. 540, 550, 112 S. Ct. 1535, 1541, 118 L. Ed. 2d 174 (1992). The problem in that case was that the government went well beyond simply opening the door of opportunity to commit the crime. Instead, by bombarding the defendant with repeated mailings over more than two years enticing him to buy the child porn and including statements that suggested it was not illegal and he would be standing up for free speech rights by buying this stuff, the government pretty much pushed him through the door. He might not have been predisposed to commit the crime when the government started, but after a two year campaign he finally gave in.
What you described does not make an obvious entrapment defense. You were the one who first put in an ad looking for a sexual encounter. One might fairly think you might be interested in paying for it since many such ads are in fact preludes to prostitution hook-ups. The cop merely responded to your ad and made the offer — it was up to you what to do about it. There was a little bit of back and forth, but nothing suggests the cop used some kind intense pressure to push you into agreeing to anything. But certainly you will want to ask your lawyer about it.