New Flower Bed Help

I pulled grass out of an area about 10ft wide along my back fence for a new planting bed. I want to plant climbing roses in the back of the bed, then daylilies, dahlias, anemone, coneflower and some other misc filler if I have a lot of room left.
The problem, and I didn't know this until I dug out all the St Augustine grass, the neighbors behind me raised their flower beds all along their fence, so the drainage goes in my yard. The grass has always been very green and lush on my side of the yard there, now I know why! The grass may love it, but will the plants? The dirt is not slushy wet, but it is mushy and smells boggy. I'm not sure if it ever completely dries out, but I assume it drains somehow because there is never standing water. I added about a cu yd of garden soil and mixed in with the boggy soil. It's still mushy though.
I'm in Houston, so I wonder if once our really hot weather gets going the soil will dry out better, and I should just move forward with the plan I had, or if I need to do something to the bed before planting anything, or should I incorporate some sort of plant that will drink up a lot of the extra moisure?
Any suggestions are much appreciated :)

You could always raise up the soil level in that area or build your own raised beds. If the ground is mushy and smells boggy, that tells me it is staying pretty wet and many plants may not be happy under those conditions. It'll dry out faster when the weather's hotter, but I'm assuming your neighbor will probably water their garden more in that sort of weather so that may not help, plus the plants are going to be in that bed year round and they won't be happy during the times of year that it's cooler and doesn't dry out as fast.

You may also be able to get help from your neighbor to put in drainage so that their water isn't collecting on your property. If water drained that way naturally then there's nothing you can do, but if their raised beds are causing more water to drain onto your property than what was there before, then they may not be allowed to do that. In many areas there are rules against changing things in your yard in such a way that it drains more water onto a neighbor's property, so they may be responsible to put in some sort of drainage to keep their water out of your yard. I'd start by talking to the neighbor and try to resolve things nicely of course.

If you need to, you could put in a french drain on your side of the fence. If you don't know what a french drain is, it is just a ditch about 8 inches wide and filled with gravel. That lets the water drain down before it gets to your flower bed.

I like the idea of a raised flower bed, but I would also put in some kind of drainage just to make sure. You could dig out a little area for decorative gravel and have the ground funnel to it. It would look nice, but help in major rainstorms.

hmm, I have some extra roof shingles in the shed. I'll dig a ditch and use the shingles as a retainer in the back of the bed to keep the dirt in the bed, then fill with rocks. hopefully that will work, however the water will be trapped there until it evaporates because I don't have anywhere to drain the water to.