32-bit ArcMap is not playing well with 64-bit AutoCAD Map
There isn't a 64-bit version although you can add in 64 bit background processing. ESRI released ArcGIS Pro, which is a 64 bit program. Have a look at the site for licensing and other details surrounding the program. It isn't a replacement for ArcMap, but you may find you're able to use a lot of the same functionality in it that you would with ArcMap.
The 64 bit background processing is a good start if you are able to run items in the background. If speed is your worry, you are also able to utilize
ArcPy modules in stand-alone python scripts as long as you have appropriate licensing.