I've gotten along with DH's ex just fine, although sometimes there have been conflicts - mostly because I've overstepped my boundaries (or at least she thinks I have) and she gets defensive very easily. I've been with DH for 11 years (married almost 7) and his sons are now 16 and 17, so I've been in their life a long time. DH and his ex got married very young (she was 19, he was 22) and had the kids 3 and 4 years later, but basically got married and had kids for all the wrong reasons.
I think it just depends on both parties and how willing they are act like mature adults and put their feelings aside for the sake of the kids. DH's ex is the one who initiated their divorce and she's always maintained that she doesn't want to harbor any ill feelings toward him and is happy that he has found happiness with someone else and even now has a daughter with me. Now whether she truly means that, or is just putting on her game face, I don't know, but whatever - I appreciate the effort. There have been many times that I have questioned her parenting skills, before becoming a parent myself, and now that I have a little one of my own, I feel bad about that - I still have my opinions but I have learned to keep them to myself. When there has been an issue, DH generally will support me and understands where I'm coming from, but hasn't always agreed with what I've said or done and ends up stuck in the middle when the boys' mom gets her panties in a twist. We both know that the boys will be the ones who benefit if we can keep in civil, and she's always maintained that she never wants to keep the boys from seeing their father whenever they want. As a result, we've been able to take them on some great vacations (including Disney World twice) and make some wonderful memories because she would rather see them have these positive experiences with someone like me and their dad than not at all, knowing that she can't necessarily provide them herself.
If I had to offer advice it would be this:
For the step-mom: Respect the bio-moms wishes. Do not tell her how to parent her kids. If you have a concern, bring it up with the dad, and have him talk with bio-mom if appropriate, but let them be the parents. Try to do fun things without looking like it's a competition. Respect the kids feelings but also expect them (and bio-mom) to treat you with respect, if you are deserving of it (not every step-mom is - sorry!). Don't talk badly about each other. Recognize that you can't control bio-moms feelings or "make" her like you or agree with you. Realize that it will be a thankless job (for the most part) but it has its own rewards. Hopefully when the kids are grown, at some point, they will appreciate everything you have done for them.
For the bio-mom: Understand that the relationship with the father is over, however it came about. Whatever bad feelings you have, try to work through them and try to let them go. Let the kids have a relationship with the step-mom so they don't feel like their loyalty is divided. Let them see how two adults can get along and work conflicts out. If Dad and step-mom have something fun planned with the kids, let them do it - don't say no or pull other stunts just for the sake of being a jerk. Don't bad-mouth the stepmom. Make sure the kids know you expect them to respect the stepmom, as they should any adult. And if the kids complain about something, don't jump to conclusions - talk it over calmly with dad first and realize that kids often exaggerate and stretch the truth, sometimes just to gain your sympathy (and that goes for stepmom too).
Have you talked with the kid's father (your husband now) about this? Why do you think the bio-mom thinks you are mean and nasty? Have you tried extending yourself and been rejected or do you keep to yourself and she assumes it's because you are being cold and closed off? Remember - it's a 2 way street and like any relationship, communication is key.
BTW, bio-mom and I are friends on Facebook...she says she gets a kick out of seeing pics and hearing stories about my DD (now 3.5 yo).