Keep talking to her.. be her support system.. call her and check up on her.. even if she gets mad at you! It's your job as her friend to help her.. even if she doesnt want it. Something like bulimia isnt something to be taken lightly.

You're a good friend for being so concerned for her. If I were you I would avoid offering to help her lose her weight through diet and exercise (although of course that is normally the healthy way to lose weight). I only say this because in her mind it might translate as you saying that she NEEDS to lose weight.
Bulimia is an emotional issue that has serious physical consequences (ruins you teeth, hair, raises the possibility of having a heart-attack, etc) all things I'm sure you know. What you should tell her is that she doesn't need to take the weight off all at once. She just brought a baby into this world and she doesn't need to immediately go back to her exact same figure. You shape changes throughout life and after having a baby is one of those times. Maybe your friend DID have an eating disorder in high-school and her body changing with the baby has re-surfaced all of those issues.
I would worry even more because she is "drinking" (I assume this doesn't mean a casual drink once in a while). So she seems to be at a point where she feels things are spiralling out of control and she's trying to find a way to cope. She could be suffering from feelings of postpartum depression that need serious professional help. I think all you can do is tell her she needs to see a doctor, hopefully he will refer her to a nutritionist and a psychologist or psychiatrist.
As well. try to help her relax in more healthy ways, like suggesting you two take her baby for a walk or to the park together. You could also babysit for her pro-bono once a week so she could have some free time to go grocery shopping or just relax. All you can do is be supportive and tell her that you've been through it and came through once you started to make some changes in your life. Don't take it personally if she wont take your advise, she has to want to make those first steps to ask for professional help.

I would just continue to be her support but I do agree with grl in the world offering to work out with her could make her think she needs to loose weight. Try to just doing fun healthy things together and offer her that support to talk about things when she may need it. Often times someone with a eating disorder will deny it or not care about your feelings on it. You cannot fix her you can only be her support.

You are a good friend. the thing is you can't make anyone eant to change. i would just talk to her about getting healthy for the sake of her child if that doesn't work tell her that you are there for her when she is ready to get better. Dont try to police her or force the issue everyday- it will just drain on you.
I have been on both sides of an eating disorder i have wanted to help friends and i have needed the help myself. There is one thing that i have learned you can't make somone want to get better. So let her know that youare there as a support, but don't expect to fix her problem. I am sorry i know how helpless you feel about this. Havinga history with the disorder yourself becareful that being with her doesn't trigger bad feelings

TINA!

Why dont you tell her to go to the gym together... you are supporting her in healthy way to loose weight. You can tell her that maybe both of you should start on a healthy diet. Try to make her feel like she is not alone on this.

If she doesn't want to stop, she's not going to stop until purging becomes too distressing or conflictual in her life. If you make yourself totally responsible for her weight, her drinking, her life, it could end your friendship. I would certainly think that expressing your concerns and care for her is always appropriate. But I'm guessing this ultimately is not about weight.