I have a few Baggallini very small cross-body bags like that and I love them. Unfortunately 2 of my favorites don't seem to be made anymore or are very hard to find any left iin stock, and they're the perfect size to fit my 5-6" readers in them and a few essentials like phone, camera, keys, ccards, etc. But the brand is very lightweight and really sturdy, well made. I dislike any with flaps generally though since items under it aren't really secure from pickpockets or if you tip it the wrong way, and it just adds more bulk to the bag. They also don't have the color selection they used to have, most usually had at least a dozen different color combos, now I'm lucky to find 4 choices, none of which I like.
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Edit: I also got them on sale, usually at ebags.com, and I never paid more than $35 US for any of them. Having a shoulder strap is a must for me as I hate having to actually carry a purse and hang onto it, worry about setting it down, etc.