Technically, if you hold guardianship and BM has no rights, then you can refuse contact and cut her out of SS' life at anytime. If she wanted guardianship so bad, she should have sought it out. You maintain guardianship which means you are to act in SS' best interest. If contact with BM isn't in his interests, don't let it happen. If you want to continue contact then you make sure BM knows to stay in her lane, that visitation is a privilege, not a right. 

Personally no I would not allow that toxicity into the child's life not matter how much they begged. It's like a kid begging for more candy, you know it's not good for them, so why keep feeding it to them? His mother is the same way!

How old is your SS? Cutting out his mother isn't the answer, it will likely make him resentful.  However, she should have supervised visits only, by someone you guys trust, so she can't fill his head with garbage.

While cutting BM out of his life seems like a good idea, it probably isn't for a whole host of reasons. But, you can control the visit length, frequency, and whether supervised or unsupervised. 
Has this child had any therapy to deal with this situation? If he hasn't, it would be a good idea.  There's a lot to work through here. A therapist who also does family sessions, in addition to the child's individual session, can help you determine the appropriate visit parameters.

I imagine,  unless bm goes into the clinker,  she will be awarded custody back sooner or later.

That is the nature of the beast. She is already building her case, more visits, more visits,,more time,,more time. So she can show the court how wonderful she is.

I am sorry you are upset and do not want her involved. She is ss mom and her rights are still intact. DH and you will have to prove she is unfit. That bar is very high.

Good Luck and welcome to ST.

IMHO since your DH is his father and you are his legal guardian, go fo zero contact until the kid turns 18.  In that time frame make sure the kids are fully seasoned with the facts and the truth about their toxic manipulative evil BM.  She gave up her rights and has apparently never pursued re-instating her rights.  Your DH and you have won parental rights to SS.  Stand on that solid ground and protect  your Skid.

We never went the guardianship route with my SS. His mom, my bride, had full physical and legal custody so we never had to go for guardianship. I was his dad. And 27 years after we started dating when he was 15mos old, I'm still his dad. He asked me to adopt him when he was 22, we made that happen.

We made sure that he had the facts and the truth regarding the endless manipulative crap that the SpermClan would attempt to put on SS as he was growing up.  Eventually our son was able to defend and protect himself from their crap in real time and would call them on the manipulation and lies as soon as they spouted them.  Our goal was to prepare him to defend himself from them and manage his relationship with them so that when he reached adulthood he could make informed decisions when they perpetrated their usual manipulative crap.  They did try it.  They attempted to guilt him into implementing direct payroll deductions from his USAF pay to help support his three younger also out of wedlock SpermIdiot spawned half sibs.  Nope, he had their number by then and has kept them in their place.  Smart kid. He learned to recognize their crap and their manipulation tells as he was growing up.  When he was in his mid to late teens we would often find him elbow deep in our Custody/Visitation/Support files after a visitation doing his own research on something they pulled that did not pass the smell test.

Growing up he went through a phase where he was desperate for them in his life and insisted that their was an explanation for their crap.  My guess is that this is the phase your SS is in.  We kept the facts flowing, reviews of the CO, court hearing recordings, full information provided for all court action, supplemental county rules, state regulations, arrest records, etc, etc, etc....   Their dedication to toxic burned through his good heart and good intentions until eventually he had to face reality that they were manipulative and just plain mean.

As hard as it is, I think that full confrontation of BM has to happen and your Skid has to be dragged through the facts, truth, data, etc, etc, etc.... so that they have a chance to protect themselves from their toxic manipulative BM.

My SS got to the point where he would confront them face to face on visitation when they pulled their bullshit out to play.  They hated that.  SpermGrandHag would call my DW and rant.  My DW would calmly roll out the facts for the Hag's enjoyment as well. Which usually transitioned the Hag's rant from claiming we were lying to SS to "you just have to roll all of that out again don't you?"  My DW would then step her through the fresh versions of the same crap from them.  Eventually, they pretty much had no choice but STFU and knock their crap off.  For some reason that never stuck. After the most recent ass baring faded, they would crawl back out from under the slime covered rock in their shallow and polluted gene pool to try to perpetrate their usual shit.  To little avail.

Stay the course, put your foot down, bring the pain, bring the facts, give the Skid the truth, and keep it all refreshed, over, and over, and over again until what is right and the facts prevail. Even in the tender brain of a SKid who arise the primary victim of the efforts of the toxic blended family opposition.

IMHO of course.

Good luck.

We recently had to block BM from YSDs phone, the constant manipulative texts back and forth were exasperating YSDs depression and causing problems with her behavior and her relationships with us.

SO isn't stopping her from having visits, but it is also a different situation legally. BM still has her rights. But just an attempt to minimize the emotional abuse. There is no need for BM to talk to YSD when she is here. There is no reason for BM to have any influence when YSD is in our home. 

Unfortunately the impact has already happened, the goal is that YSD can make some progress in therapy by minimizing BMs brainwashing. 

If you decide to let her see her son, I would do so only through a supervised visitation center (at least then you could be sure that she isn't pouring out her venom to him) and I would make her foot the bill for it. I think you'd soon see how (un)important her son is to her when it hits her in the wallet.

Birth mom gave up her rights...

She has no standing for anything. Let her file in the court.

This is nuts.