Congratulations on your bid! Will you tell us which sorority? You don't need to tell us your chapter/school.
Your level of involvement probably depends what you are able to do as a new member vs. initiated member. Try to go to every event you can, take full advantage of the semester in your sorority. Remember that membership truly is for life, and as an alumna you can join an alumnae chapter in your city, volunteer in an advisory capacity for undergrad chapters, etc. When you go alum, you will probably receive information on how to stay involved, and if you don't, request it!
Are there any committees you can join to assist with planning events? Can you offer to help with preparation for Fall Recruitment--this can be especially rewarding, as you are then a part of preparing for the future of your chapter, even though you won't be there for actual recruitment.
In terms of growing closer to your new sisters, spend as much time with them/at the house as you are able--take advantage of casual socialization opportunities. Do a lot of girls get together and watch a particular show every week? Join them! Things like that.
Enjoy your last semester of college