Trying to Understand Relativity (part 6)

This relativity business is pretty confusing.  I've been thinking that my thought experiment might be a little easier to follow if I made it a little less abstract.  With that in mind, I think that I should give the people in house A and house B actual names and identities.  We'll call the guy in house B "Bob", and we'll call the person in house A "Ann".  Yep, the person in house A was a woman the whole time!  Bam! That's what they call a plot twist.  Bet you didn't see that coming.  You see, Ann had just called Bob to tell him that she was lonely and wanted him badly.  That's why he was pushing the light barrier to get over to her house.  It all makes sense now.

Please.  No comments about the Freudian symbolism in this picture.

So anyhow, when we last left these two, I had just made a nice break in the case.  I had said that if Bob made the trip between the two houses at a speed which allowed him to cross the light-year between them in a year and one day, then it would appear to Ann that he was making the trip in one day, unless you accounted for the constant velocity of light.  By taking that into account, time itself would have to expand.  I speculated that the trip would have to take 365 years from Ann's perspective to keep her view of the image of Bob's ship from exceeding the speed of light.  (If this sentence sounds like gibberish to anyone new here, please refer to the Relativity tab above.  It'll probably still sound like gibberish after that, but you'll have the satisfaction of reading 5 other pages of gibberish.)       

I want to try something to test the math here.  It's not that I absolutely need to know the math.  I'm not going for a PhD in relativistic physics.  I'm just trying to grasp the basic concept.  But if I can check my idea against the percentage of distortion that relativity actually predicts, then I'll know if I'm on the right track.  

Okay, let's say we slowed Bob down to a speed where he was crossing a light year in a year and 6 months.  That would put him at about 75% of the speed of light.  Without taking the constancy of light into account, the trip would appear to Ann to take 6 months.  This means that she would have to see the ship coming towards her at twice the speed of light.  Now then, going by what I said last time, in order for her vision of the ship not to exceed the speed of light then the trip would have to take 2 years from her perspective.   That makes the trip 1 year and six months for Bob, and two years for Ann, and the ratio of distortion would be  approximately 1:1.3 at 75% the speed of light.

So this is basically what I'm doing here: I'm considering how many times faster than the speed of light Ann would have to see Bob's ship going for her to witness the trip without any time distortion.  Then I'm multiplying that number by a year, because there's one light year of distance, so light at it's constant speed should take a year to cross that distance.  Then I'm comparing that result to the time it actually takes Bob to make the trip.  In that manner, I'm coming up with a ratio between time for Bob and time for Ann that expresses the distortion mathematically.  Again, in this case 1:1.3 at 75% the speed of light.

At this point, I feel like I've thrown this whole thing together with duct tape.  It can't be right, can it?  Well, check out this handy little chart showing the distortion courtesy of Zayini at wikimedia commons:

I was forced to attribute this picture at gunpoint.  Sorry.

The numbers running up the left of the graph show the ratio of distortion, while the numbers running along the bottom show the percentage of the speed of light.  You can see that between 70 and 80% the curve hits at around the 1.5 mark.   So I'm a little off.  My formula is predicting that Bob's 18 month journey will take 24 months from Ann's point of view, but the chart is suggesting that the journey would take 27 months from Ann's perspective.   I'm off by three months.  That might not seem like much, but it definitely shows that my formula is wrong.  

Last time I think I got a clear glimpse of the time distortion.  I can at least see not how it's possible.  Progress is being made.  But I've still got some work to do, figuring the finer details of how it works.  The thing to focus on now is how Bob's 18 month journey at 75% of the speed of light can come out to be 27 months for Ann.  This handy chart is telling me the result I'm supposed to get.  I just have to come up with an understanding which produces this result.  Should be pretty simple, right?   

Thoughts?  Anyone?