I took three people to the range this year and assisted a friend take two others to the range as well. Everything went well as several of them are making plans to purchase their first gun and plan to shoot with me again in the next month.
I don't do this very often and actually average about one new shooter a year. More often, a fellow shooter will want to introduce his or her friends and ask me along to assist. I live in SoCal and I guess it's different here versus other parts of the country. There are actually a fair number of gunowners who have one or two guns and very rarely go shooting. Along with that, a big problem is that gun ownership is rarely talked about so people get nervous when it's discussed.
One guy has had an SKS for ten years but his own brother had no idea he owned a gun. Another said he was surprised when after he went shooting with me, he talked about it and found out a lot of people he knows own guns. It's like people here are afraid to "out themselves" as gun owners until they know you are gun friendly. I just look at it as another obstacle I need to keep in mind when I try to add more to the flock.
As for refusing an offer, people usually agree with some excitement or they refuse awkwardly and don't really give a solid reason. I think it's irrational fear so I try to present myself as a safe, responsible gun owner who is knowledgable. I even thought about getting NRA certs just to ease the fears of the newbies and/or their significant others.
For the guy who initially refused, I just told him the offer has no expiration date and he can change his mind any time. I'm a horrible hunter but when I get lucky and harvest game, I offer some of it up to the fence sitters. When they invite me to hang out, if I have plans to go shooting, I let them know I cannot because I am going shooting/hunting/competition/gun shopping/etc. Basically I try to get it into their heads that its a normal everyday thing to do.
Once they get used to the idea that responsible gun ownership can and does exist, curiosity gets them
On a side note, I once took a close friend's 11 year old kid sister to go shooting. She also has a 10 year old kid brother but he's a brat so he wasn't invited. Anyways, the 11 year old sister is a good kid so I told her "even though you are a kid, I can see that you are very responsible and you have earned my trust with your good behavior so that is why I am willing to teach you to shoot. I've met boys twice your age and I would never take them shooting because they are irresponsible."
So the three of us went shooting and it worked out great - the kid shoot very well and we took some pictures of her holding an M4gery with fake suppressor. Funny how after that, the bratty kid brother started behaving very well and trying to show he could be responsible as well
I don't do it more often because I am very picky about who I invite to go shooting. However, the SKS owner mentioned above wants me to take him and his girlfriend shooting soon so I call it progress.