You have to use your turnips against her when you get the opportunity to if you want to get in. Try not to give jiggs an idea with what you're going to do with the turnips either because it will give you A LOT more to work with if youre not predictable with them.
If you keep as close as you can to jigglypuff and bait her in with turnips-- (because she wont come close to you otherwise), you'll have the upperhand in most situations. It works suprisingly well for me.
Try this,
Pull out a turnip, KEEP it in your hand and try to approach jigglypuff when shes spamming WoP, dont roll into her either. When shes backs up after she hits you/or lands behind you and becomes out of grab range, throw your turnip at her (since sheild grabbing never really works on jigglypuff players who space their aerial approaches on you, which basically is the idea behind WoP) and pressure youself into her, get as close as you can. When you have a turnip in your hand it will pressure jigglypuff to get close to you (only because she cant compete with projectiles.. and basically when that happens, you have to play sheild games with her. You have to practice doing b-air/n-air/f-air and short/full hop d-airs out of your sheild.
Its better to not compete with her in the air. She has more priority. Try to keep it on the ground. If you know how to DJC your aerials it will help alot in this match up because it will bring you to the ground faster than actually jumping out of your sheild to N-air her (which will leave you vulnerable) just make sure you L-cancel if you try to DJC because theres alot of lag after peaches aerials which normally lead to nasty consequences..
Heres an example.
http://youtube.com/watch?v=ITW4kg9FYs0
http://youtube.com/watch?v=N0JjBXIZXcE