Yep, that's it. Don't know which. I googled it and there are over 650 subspecies. I don't think it could be invasive because my Chocolate Lab is quite adamant about eating it. It's actually a medicinal plant for liver, kidney, bladder, and anti-inflamitory and a good detox plant.

Being invasive isn't related to whether a plant is edible or not. Garlic mustard is very invasive in N America and also quite tasty. According to this https://www.invasiveplantatlas.org/subject.html?sub=5656 Galium aparine is invasive in some states.

Look to me like sweet woodruff. It get a small white flower in May

Maybe because bedstraw/cleavers and sweet woodruff are very closely related :-) But if the plant attaches itself to dogs or your pant leg, then it is the Galium aparine and not Galium odoratum.

Says it grows in wet shady areas and I only have 2 small areas where it will grow, so it shouldnt take over my yard.

Don't believe everything you read :-) The Galium aparine pops up wherever it feels inclined in my garden - sun or shade, moist or dry. The sweet woodruff does prefer shade, but it is also growing in my garden in very sunny positions as well. I find the sweet woodruff much more aggressive than the cleavers, as it is perennial and spreads primarily via roots.....a very dense and all encompassing flat root system!! Removing a dense planting is a lot like rolling up a carpet :-) The cleavers are an annual and a once-and-done weeding situation unless allowed to go to seed.