compost helps improve drainage and vastly improves soil. ideally you'd want to mix as much compost with the native soil rather than putting it just on top. i'd also mulch with something like oak leaves instead. leaves tend to be good at blocking water. 2-3 inches of compact leaves will block at lot of water and can help direct it away from the base of the plants.

It sounds like you are suffering from the dreaded "bathtub effect" - even though the top of the soil is amended, underneath is tight clay and water is running in to the bed and has no where to go. And you are right - this is a problem for plants there. Especially for shrubs like roses that have deep roots.

Here are my suggestions in order of bang-for-buck (or bang-for-backache).

1. Raise the bed. Even if you only raise it 6" with a border around it, that will make a big difference to the plant. If you were doing annuals or vegetables, this would probably solve the problem. But you might need to an additional remedy for the shrubs - probably 10 to 12 inches would be ideal, but that is a lot of work and will radically change your landscaping.
2. Put in a drain right next to the bed. Maybe there is a walkway, or just create an 8 or 9 inch French drain parallel to the raised bed. Fill it with gravel or stones so gravity will move the water away from the bed.
3. Add some organic mulch like chopped leaves + coffee grounds + grass clippings as a thick mulch to the bed. This will break down pretty much over one or two seasons providing a rich and fast-draining topsoil for the shrubs. (Keep adding more mulch as needed.)

Doing all three of these would probably work wonders.

In short - you are not going to be able to change the actual properties of the soil without more work that it will be worth (not to mention the damage to the structure that more digging will cause). Better to raise the surface, mulch the top, and give the water a legitimate path to follow.

My two suggestions although don't know much about roses ( I let other household members work on those): as others have said, mulch mulch mulch. I'd include something on top that's drier - bark/wood chips - as they'll both cause some of the water run off, and buffer by absorbing water/releasing it over time. The other suggestion: plants that put down deep, thick, non-woody roots, like tillage radishes. They might have the wherewithal to get deeper down and over the next season die and leave the root channels for drainage.

Thanks everyone! I bought some compost yesterday from my local garden store. It’s Black Kow mushroom compost. The store employees said it was the best thing for breaking up clay and worked really well. I like it a lot as it looks so rich and has no smell. So, I started to work it into the soil and have discovered that in a few areas it looks like the water is just sitting there and coming out of certain crevices. I dug about 10in deep and that’s when I noticed it. I stopped digging so the soil can dry out in the over saturated areas and will start again once dry. I will do my best to mix the compost in thoroughly.

I’m not sure I can build up the soil as it will make the garden look odd, so I’m left with tilling it and then putting mulch on top. I don’t usually till unless there’s a reason for it, but I’m hoping me tilling it once and adding a lot of organic matter will help drainage. I thought about a French drain, but the area is so leveled that it will take some work. I don’t have the money for a French drain right now, but I will get it done in the future.

I went outside and took a really good look at that garden bed. It seems like the garden has a very slight downward slope towards the small area that is flooding. Seems I will just need to add more garden soil to level it out a bit. I’ll dig a trench to direct the flow of excess water as well. Hopefully this helps with the flooding. Thanks everyone for the help!

Well, just an update. I bought Black Kow mushroom compost and Espoma Soil Perfector. I mixed it very well into the soil and then built a mound to place on top of the rose bushes. They are doing much better and the soil is becoming less soaked with heavy rain. We had 4 days of heavy rain this week and while the ground did get soaked, it wasn’t as bad as it was and the roses are still pushing out new leaves and blooms. I’ll keep adding compost around the roses each year and mulching like I normally do. Thanks everyone for the help.