First off -- why do you believe that your milk is not enough for him? Babies rarely choose to starve themselves, so if he's very hungry, he WILL be willing to take the bottle.
But if your supply is low, the better solution would to try to increase it. How often is baby nursing? A typical 4 month old is still nursing every 2- 2 1/2 hours during the day, usually with 1-2 longer stretches at night. (8-10 feeds in 24 hours.) So if he's nursing less than that, try offering the breast more often. If he doesn't want it, trust that he's getting enough. If he DOES nurse more, he'll get more milk and the more frequent stimulation will increase your supply.
As for the bottle ... it's generally recommended that if you expect to want to introduce a bottle at some point, 6-8 weeks is the best range for it. Much earlier and baby is likely to get nipple confusion. Much later and they usually (as you've found), refuse it.
If you still feel you must start a bottle, try having someone else offer it. Babies often refuse a bottle from mama (they know the breast is available), but will take it from daddy or a caregiver. (You need to be completely out of the room.) You may also need to try different nipples, different formulas, different positions while holding him, etc.
If he flat out refuses it, you could wait a couple of months and try a cup. Or, while he's still pretty young for solids, if he's able to sit up and eat from a spoon, you could try a bit of solid food once a day and see if that makes a difference for him.