swimmer seeking bike advice

I plan on taking this pretty seriously so I'm wondering how much should I be looking to spend on a bike?

How much do you have? Add $1000 to that. How seriously do you want to take this? Entry level road bike will cost you ~$500, you coud probably spend $10K without problem. First step: establish a budget, step 2, educate yourself, step three, shop your a$$ off and compare.

Are the differences between a lower end and upper end real significant and worth the investment?

Yes. But you do get to the point of diminishing returns wher you're paying more for minimal weight savings that you are for real efficiencies. I'd recommend you get at least an Ultegra-level bike if you plan to take "this pretty seriously." Then invest in wheels rather than more bike. Of course, if you have the budget, go for it all.

Are there any other accessories that are must haves for training?

Clipless pedals and triathlon cycling shoes are a must, aerobars as well.

There's an old "proverb" that you should spend a dollar or less per mile for each mile you ride in a year.

there are a few price points where the bikes are substantially similar in terms of weight, and component quality

<$500 is pretty rare for a raceable bike

$500-$800 you find some entry-level road bikes here. These will have heavier frames, and lesser componentry, but they will be quite servicable and safe

$800-$1000 is a pretty competitive price point for budget racer type bikes, occasionally you find a piece or two of eye-candy componentry (maybe an Ultegra rear deraileur, or a carbon bladed fork)

$1000-$1500 Here you'll find bikes that are made to be raced and a significant jump in component quality, frames start to get  lighter, there are frame materials besides aluminum available

$1500-$2500 This price range I think represents a top-down rather than a bottom-up approach. Here you see bikes that are substantially the same as those that cost twice as much, except some of the high-zoot bits are replaced with less exotic stuff

$2500-$5000 Damn fine bikes, essentially what the pros ride, in some cases exactly what the pros ride.

$5000 and up......as good as it gets.

Make sure to budget for helmet, tools, pump, shoes, computer, etc.

A lot of folks reccommend Joe Friel's "cyclist's training bible" (I am not 100% sure of the title.

I started on a $300 hybrid that my future hubby bought me for a college graduation gift.  I needed something better so my in-laws offered $1k for a bike for a b-day gift (!!!!!).  I found a used '01 Trek 2200 w/cat eye computer for $750.  I have since added speedplay pedals, clipless tri shoes & 2 new seats (I passed the first one to my hubby when I upgraded).  You will also have to spend $ for bike clothing, helmet, gloves, drink holders, etc. so it can really add up. 

Anyway, I love my bike.  It retailed for ~$1,800 new and was kept up pretty well.  I'm doing okay without the aerobars, but the clipless pedals are fantastic and I wished I hadn't gone so long without them.

I think a well-kept used road bike is the way to go, especially starting out.  When I upgraded to a road bike, I just didn't know enough about bikes in general and how road bikes feel to make a really good decision about what I would like best in the end.  I mean, I felt hunched over and uncomfortable on all of them. ;-)

If/when I decide to upgrade again, it will be to a tri bike.  Fortunately, Hubby is my same height so I'll pass down my bike to him.  The best thing, though, will be that I'll finally know enough about bikes and how I like them to feel that I'll be able to make a good decision with such a large wad of cash.