If you have the bag across you, if you have it draped on one shoulder, you would maneuver in front of you, don't waste time by taking it from across your shoulder. If he is trying to hit you, you can grab the purse and slam it up hard into his nose, this is a great block. Also if he is coming at you with a more deadly weapon, that could puncture skin or stab you, you can put your purse between him and your body to protect yourself from the weapon. Better that a knife or a sharp weapon hits your purse instead of puncturing a vital organ or causes serious harm. You can do this with a few different types of bags, purses or backpacks.
A cell phone. Obviously one of the best helps a phone gives you is your ability to call for help. However you should be aware that you can actually use it as an effective weapon. It's hard, durable and compact. You have it at home, and usually on your person, or in your bag. You are going to take it in your hand like you are holding a bottle of water and you are going to hit hard into the attacker's groin, right between his legs.
Swing hard up into his groin. If you can hit him multiple times aim for the groin, again and again. Hey guess what you can always get a new phone! If he attacks from the back, swing the phone down and into his groin. Even though he may attack you from the back, you will still have your arm up in a defensive block. In one moment he may be attacking from the back and a moment later, he is attacking you from the front, so keep your blocking arm, is still up and ready. If you need a follow up strike your blocking arm is ready to strike.
Also if he is facing you, and he is in very tight, and you don't have room to swing it, hold the phone in both hands by the ends if you can and slam the phone straight into his nose. Hit him multiple times if you can manage it. Hit him hard in the eardrum. If you are holding the phone in one hand, the other arm comes up as a blocking arm. The last resort, drive a straight shot into the side of his head at the (temple area.) That will hurt. If you still have your phone after all of that, and it's still working, keep it as you run and call for help.
My next item is a hairbrush. Brushes come in many sizes and shapes, some with handles and some without. If you can grab a brush without too much difficulty, the brush would be a great weapon, one with a handle can be easy to grab. You can hit him in the groin, nose, knee cap, or side of head (temple area) or eardrum. For the discussion assume that we are hitting, or striking in some of the vulnerable body points, groin, nose, ears, eyes, side of the head, and knee caps.