While I second the recommendation to have this done at a bike shop, just for your information, this post adds a bit of information that the others haven't stated.
There are two parameters to consider here. The one you are missing is the type of bottom bracket shell. There are numerous press fit bottom bracket shell standards. For example, you might have a PF30, or BB30, or B86 shell. If you have a Trek with a press-fit BB, it's a BB90. If you have a Cervelo, it's BBRight. They all vary as to the diameter of the shell and the width of the bottom bracket. Anyway, you can Google the model and year of your bicycle to find out.
From there, a bottom bracket that fits in your BB shell may be designed for a 30mm spindle, a 24mm Shimano spindle, a 24/22mm GXP spindle, or one of a number of other types. You could just buy a BB that for your shell that specifically takes a 24mm Shimano spindle. As a side note, I believe that at least some BBs designed for 24mm cranks will just supply a 2mm adapter for one side of the GXP spindle. GXP spindles are 24mm, tapering to 22mm on one side. I forget which is the tapered side. Nonetheless, this is why you can’t shove a Shimano crankset into a GXP BB.
If you have a BB that takes a 30mm spindle, there might be adapters to enable that to take a GXP spindle. Wheels Manufacturing makes a 30mm BB to 24mm axle adapter, as well as a 30mm BB to GXP axle adapter. The downside with adapters is that they might increase the chance of creaking - creaks occur whenever two components don't fit together tightly. When these adapters, there's a possibility that they might not be manufactured quite to tolerance, and creak as a result. I would probably trust Wheels Manufacturing on average, though. If you get a BB for 30mm spindles, it may sacrifice some bearing size compared to BBs designed for smaller spindles. In theory, that could reduce the expected bearing life. Getting a BB for a 30mm spindle would, however, enable you to change to a different crankset if you desired (e.g. some nice power meter or carbon or 1x cranks with 30mm spindles go on sale and you want an upgrade). I'd not worry too much about this issue, unless you know you might want a spider-based power meter (otherwise, you could just have strain gauges mounted on the left side or both sides of the Ultegra crankarms, but read this thread if you do).
As a side discussion, why would SRAM make not make a straight-up 24mm spindle? Possibly, to get around Shimano's patents. However, I believe that Shimano's Hollowtech II design was released when the patent on an earlier crank design expired (the Sweet Wings cranks, if anyone's interested). So, I'm not sure what the patent status is for 24mm spindles in general. Also, why do 30mm axles even exist? In theory, the larger diameter enables the axle to be made of aluminum, thus saving weight. It could also be stiffer than a 24mm steel axle. These are not practical differences, really.