Errr... not exactly. I will go to bed. = in this case, it's an imagined future action. You've made a decision/promise to go to bed, but the action remains hypothetical. I'm going (to go) to bed. = I added "to go" to make the sentence clearer. "I'm going to bed" is a statement about your current action. The future form is created using "to be going to (action)". You use this when you have a plan or intention for a future action. You use the "to be going to (action)" form when you have evidence to support the future action. That is, you are observing the present action and making a prediction based on that. "I'm getting to bed" = this is not in common use; maybe in some regional speech, but it sounds strange to my ears. I'd correct it to "I'm getting into bed", which is a current action, not a future one. In both cases, "will" and "going to" must be followed by the future action. In your last two sentences, you didn't give an action - only a location.

I'll go to bed implies that you will do it in the near future - possibly right now, but not necessarily. I'm going to bed and I'm getting to bed both imply that you are in the process of going to your bed and sleeping right now, or will be immediately.