Is HC-05 Bluetooth adapter suitable for logging fast?
"HC-05" is a tag used for many Bluetooth modules, and they aren't all born equal. Having said that:


HC-05 modules can be configured to use a UART speed of 460,800 kpbs, in some case even higher.
HC-05 modules support Bluetooth 2.1 including Enhanced Data Rate (EDR). EDR has a theoretical maximum data rate of 2.1 Mbps.


You mention a limit of 10ms. Does that mean sampling every 10ms (throughput) or sampling every so often and transmitting the result within 10ms (latency)?

Both should be possible:


Throughput: If data is sampled every 10ms and your sample consists of 20 bytes of data, a data rate of 20,000 bps is required.
Latency: A maximum latency of 10ms for a packet of 20 bytes is achievable. Note that the HC-05 module does not know when a packet starts or ends. So it has a heuristic for determining how much data to collect and when to start transmitting. You have to test if that is a problem for your particular module. I don't expect so.


The reason that your module feels slow is that the default UART speed is usually 9600 bps, i.e. rather slow.

Update

The FTDI232 will also introduce a delay. As a USB slave device, it may only talk when asked by the USB host, which it does every 1ms.

Most likely, the slave will receive a single byte and forward it to the host when asked. After that, there is a communication pause of 1ms. By then it should have received several bytes and transmit them in the second USB packet. So expected a delay on the receiver side of up to 2ms for for 20 bytes of data.