The short answer? Yes. You can replace the battery yourself.
As a matter of fact, iFixit has a guide to show you how to do just that. Located here:
MacBook Pro 13" Unibody Mid 2009 Battery Replacement
And yeah, the battery being "manually inaccessible" is a complete fabrication. Though Apple does tend to try to make it as difficult as possible by throwing as many obscure screws with uncommon heads of variable sizes as they can find into their machines.
You'll see what I mean when you read the guide.
This particular model uses the illusive Tri-wing Y1 Screwdriver to try to keep its owners out. Luckily for you, the iFixit store happens to sell the tool you need (you know, in case collecting obscure and rarely used screwdriver heads isn't a hobby of yours).
Here it is:
Tri-point Y1 Screwdriver
They also throw in a bunch of randomly assorted Phillips head screws. More common, but iFixit sells the tool for that as well just in case:
Phillips #00 Screwdriver
The price of those two tools plus shipping and handling plus the price of a few hours of your time should at least be marginally cheaper than Apple's battery replacement service.
Oh, and here is the battery if you don't already have one:
MacBook Pro 13" Unibody (Mid 2009 to Mid 2012) Battery
Good luck. And happy hunting.