As far as feeling safe and secure, my husband and I honeymooned in Bali in June of this past year, and we couldn't have felt more safe. In fact, the drivers of our cars would point out where past bombings had taken place and then tell us how security has been ramped up and what other measures are in place since then. We felt that there was plenty of security present and that the locals acknowledged that there had been bomb blasts in the past, but we did not feel overwhelmed or threatened by the presence of security. Although I hesitated to visit the part of Jimbaran beach where a bombing had taken place in 2005 (lots of fish restaurants on the beach that looked good but we skipped!), overall I felt quite comfortable. I would certainly go again!
I will note that we also stayed away from touristy spots like Kuta. We stayed at the Four Seasons (both Jimbaran and Sayan) and did our activities nearby to our hotels.