Why does cropping in lightroom before I export, decrease my file size (and quality) so drastically.
Cropping does not decrease quality.
if you have an image of a certain size, and you crop it, of course it will be smaller.
The megabytes are meaningless, they do not indicate the quality of your image. Stop looking at megabytes. Instead look at the pixels in the image, that will tell you if you have enough pixels for any given purpose.
If you export a cropped image then that exported image will be smaller than the original. That's what cropping does. You should concentrate on the pixel dimensions of the images rather than size of the file. For example, if you are going to have an image printed on a page and the image is going to be 8 x 10", then the pixel dimensions should be 2400 x 3000 pixels. Multiply the desired size by 300 (PPI, pixels per inch) in order to determine how big the image can really be and still provide good quality.
Any advice on how to crop without losing my image?
I've tested bridge, and photoshop for quality decrease after cropping and they both maintain their size and quality.
If you think that cropping in LR and cropping in Photoshop are resulting in different quality and image sizes, you are looking at the wrong numbers.
Cropping does two things: (1) it changes the shape of the image, for example from 4x6 to 8x10, and/or (2) it changes the composition of the image. Either way, what you are doing is discarding pixels.
The size of a digital image is measured in pixels, not inches, not megabytes. After you are done discarding pixels by cropping the image, you later have the option to resize the image by increasing or decreasing the number of pixels in each direction. Reducing the image size is relatively simple. Increasing the image size by inventing new pixels involves some rather complex math.
Your original image stated off with a fixed number of pixels, like 6000x4000, based on the size of the camera's sensor.
How many pixels were left after you were done cropping?
Did you resize the cropped image to a different pixel size? If so, what pixel size?
When you saved the image to a file, you got to pick compressed or not compressed. Some compression is lossless. Some, like JPGs, is lossy meaning that you will lose some data so that the file is of smaller megabytes. However, megabytes cannot be used to judge the quality of an image.