No worries. So this answer won't cover everything, but I'll go off of what I think addresses your current situation. The sound quality from the laptop would certainly be acceptable, but definitely not stellar. I would be shocked if the headphone input on your laptop was connected to a good circuit so there is no reason that Bluetooth can't sound even better. Saying that it depends on the Bluetooth chip in your laptop and what codecs' it can use. AAC is excellent, every bit as good as Apt X, Apt X HD in my experience. So if you have decent Bluetooth with your laptop the Sony XM3 is very good, I use the XM3 myself. However, you can easily make the XM3 sound better as the stock signature is rather muddy due to excessive bass energy. Frankly it sounds very underwhelming stock, and I like strong bass response.
I would strongly encourage you to find a system wide EQ that you can install on your computer, or by JRiver Media Center and use the WDM driver option as it allows you to take the audio stream from your web browser (Spotify in your case if you use the web based option) and process it through JRiver so you could use the built in parametric EQ. Regardless of how you achieve it, absolutely you need to experiment and trim the bass down with the XM3. Once you find the proper attenuation you will hear just how good the XM3 can sound. Once the bass muddiness is cleared up you will have a more clear and balanced signature with solid bass response.
When I first received my XM3 I was going to return them right away as they sounded like such a muddy bass mess to me, but I decided to try equalizing them instead and I am very pleased with the results. So if you don't want to spend any additional money, and you may not need to, try cleaning up the XM3 first and reevaluate. If after that experiment you still aren't satisfied there are plenty of great options available to you such as adding a USB DAC/amp, but depending on your needs/goals, you may not even need to do that.
EDIT: Just noticed that you didn't mention which Sony BT headphone you used. Not sure why I thought that you had said you were using the XM3. I must be confusing you with another poster somewhere. My apology and my answer may not be very useful in this case. What headphone model from Sony are you using?