Given the choice between the Bodyguard and LCP I went with the Bodyguard. Like the feel and look of it better, and it offers more features than other .380's. Plus it's not as punishing to shoot at the range. Added a Pachmyer grip and it's a "fine" pocket gun now. HOWEVER...if you're open to other options in .380 I will suggest the Glock 42!
Just picked one up for my wife a month ago. She is VERY recoil sensitive and has small hands. The Glock fit the bill to the T! Felt recoil is almost nothing because of the dual recoil springs (making follow up shots more accurate). The trigger is the same as any Glock, and if you're not one whose prone to limp wristing you can forget about those bad reports of failures to feed. My wife experienced it, yet when I fired right behind her...no problem. Once I helped her correct for that she was "rollin". I'm thinking of getting one for myself.LOVE the gun, and if I were choosing my first .380 now, there's no question it would be the Glock.
If you're not tied down to the Glocks, the 9mm Kahr CM9/PM9 are the same size as the Glock 42, and provide more firepower than a 380. The 42 is certainly a nice pistol, but I think Glock missed the mark by making it a .380 in the same size as a LOT of pocket 9mm pistols out there.