Bluetooth Low Energy (BLE) master for Arduino

I'm very new to BLE, and looking for some advice.

I'm looking for a BLE module for Arduino that can run as a bluetooth master. I want Bluetooth devices (slaves) to connect to it. Devices like this handy bluetooth button:

Then, the Arduino would translate button presses into MQTT and publish via ethernet shield (Wiznet 5100). So, the additional constraint is that the Arduino BLE module not use SPI, since the ethernet shield uses SPI and it's a pain to use the shield along with another SPI device.

As an example, I see this RedBear BLE shield:
http://redbearlab.com/bleshield/

It's SPI, so I probably can't use it with the ethernet shield. But also, the way it's used makes me think it's mostly used as a slave device, not a master. So it won't be able to receive data from the bluetooth button I'm looking at. See next link

https://lilyhack.wordpress.com/2014/02/03/ble-read-write-arduino-raspberry-pi/

If anyone can give me some advice, I'd appreciate it.

EricExperiment:
So, the additional constraint is that the Arduino BLE module not use SPI, since the ethernet shield uses SPI and it's a pain to use the shield along with another SPI device.

This is nonsense. SPI is a bus for multiple devices. As it happens, a bluetooth device normally connects to a serial port, so you should be able to skate around that sort of paranoia quite easily.

As an example, I see this RedBear BLE shield:
http://redbearlab.com/bleshield/

It's SPI, so I probably can't use it with the ethernet shield.

See above. It is probably configurable to be a master but if they won't tell you it is don't buy it, as there are others that are.

Nick_Pyner:
This is nonsense. SPI is a bus for multiple devices.

Yes, SPI is a bus for multiple devices. But it relies on all devices exhibiting good behavior on that bus. I’ve read from multiple sources and experienced it myself that the Wiznet 5100 ethernet shield does some weird stuff with SPI pins when CS not selected.