Bluetooth operates in the 2.4 GHz band, the same as common WiFi.
The wavelength is roughly 125mm, so a 1/4 wave ground plane antenna just about 30mm.
A WiFi antenna from a laptop may work (they are cheap on ebay) but due to the frequency the connections must be very! short and the antenna cable would need connecting in place of the PCB antenna loop or zigzag track.
eg. The cable inner to the feed point or coupling capacitor, and cable screen to the ground plane, with ideally no more that 2 - 3mm separated wire from the coax.
Note that you do not want any kind of "high gain" antenna as they rely on being directional, a bit like adding a reflector or lens on a lamp. The ideal antenna for bluetooth is omnidirectional, so moving around has minimal effect.
The downside of a laptop antenna is that they likely are slightly more directional; they are normally used in pairs (or more) in different orientations, with the wifi module selecting whichever antennas are working best at any instant (diversity), or even using multiple ones simultaneously or for beamforming on some recent types.
With only a single antenna point as on basic bluetooth modules, there will always be some nulls; it has to rely on signal reflections and frequency hopping, which can move the nulls to some extent.
Post a picture of the antenna on the bluetooth module you are using?