There is a lot of press about flash crashes, such as this one. Have there been notable "inverse" phenomenons, where the market sharply bounces up, only to recover close to its initial state a few seconds later?
Yes, have a look at Johnson, Zhao, Hunsader, Qi, Johnson, Meng and Tivnan's paper Abrupt rise of new machine ecology beyond human response time. They studied crashes and spikes (what you call "flash bubbles") in exhaustion to conclude that there's a substantial number of trading firms whose algorithms form swarms (they call it crowds) which collectively pursue the same target.
We find 18,520 crashes and spikes with durations less than 1500 ms in our dataset, with examples of each given in Fig. 1A (crash) and 1B (spike). We define a crash (or spike) as an occurrence of the stock price ticking down (or up) at least ten times before ticking up (or down) and the price change exceeding 0.8% of the initial price, i.e. a fractional change of 0.008. We have checked that our main conclusions are robust to variations of these definitions.