Many folks drill into others that adapters (or certain types of connectors) are horribly lossy and should be avoided at all cost. What they fail to mention is that while some are more lossy than others and use of multiple ones will add to the loss, unless you get some very low quality ones or install them poorly (or simply go crazy with the quantity), you probably won't notice the difference unless you run the system through some hefty analyzers.
Using an F to BNC then a BNC to UHF instead of a single F to UHF adapter will probably make no noticeable difference. A very noisy, but readable signal with the two adapters will probably be a very noisy, but readable signal using only the single adapter. You'll probably have more of an issue with the added weight from the two adapters than you will with the signal loss. This is probably remediated fully when you secure the coax to the mast below the antenna (remember to use UV resistant tie-wraps!) so you can ignore that problem as well.
To help demonstrate this, I have an antenna with a mini-UHF connector that I generally use with one of my Motorola Spectra radios. When I need to use it on one of my scanners, it takes a bit of magic to convert that to BNC since the mini-UHF is not that common outside of the Motorola world. To handle this conversion, I have a female mini-UHF to female mini-UHF adapter (basically a gender changer) that goes to a male mini-UHF to female BNC adapter, that then goes to a male BNC to male BNC (another gender changer). Quite often this then goes to one or two 90 degree BNC adapters to reduce the strain on the scanner's antenna jack. Guess what. The signal on the scanner is pretty much the same as on the Spectra. Would I advise doing this on a regular basis? No, of course not. My normal scanner antennas terminate in a BNC directly, but for a temp addition when I need an additional scanner (or more generally need to have my handheld radio on my desk and don't need the Spectra) this long adapter mess does the job and does it sufficiently well.