Is Bodrum worth it? I think if you catch good weather April and May it can be fun, but I can't imagine Bodrum without a nice swim, and for me that starts mid-May at best.
For the dates you are thinking of: It will be nice mild weather, no traffic, mostly quiet around places you go to, all restaurants will be open. So you can eat good food, go on hikes, take a boat tour etc. If you are looking to just read a book and relax you will have a good time in MO in Bodrum. If you want to experience summer, looking for more nighttime fun and swim, you will get bored real quick.
Personally if you do not mind taking a few plane rides and packing, I would do Bodrum for a few days and Cappadocia for 2-3 days if you haven't been before. It is a much more unique experience than what you would get in Bodrum, and both areas are very safe.
About MSPEconomist comments, I personally think he was joking and will not take it seriously as it is one of the most ignorant things I have heard about Turkey lately.