I agree with Steve Perry... your best bet is probably to keep handholding those shots and simply use a faster shutter speed (you may need to increase your ISO to be able to do so).

I've seen folks use a "shoulder stock" type rig for that sort of thing, too.... though usually I think it's with lenses longer than 300mm.

For extended shooting sessions, I've used monopods... One I have fitted with a medium sized ballhead, the other simply mounts directly. However, ALL my longer telephotos have tripod mounting rings: 70-200mm, 300mm, 100-400mm and 500mm. While it's possible to use a monopod fitted to the camera body instead of the lens, it's a lot more comfortable with the tripod ring, which also allows a lot more convenient transition from horizontal/landscape to vertical/portrait orientation. On my monopod with the ballhead, the head can be "tipped off to one side" to re-orient the camera, but that's less well balanced. AFAIK, this is not possible with the "pistol grip" style ballheads shown in some of the previous responses.... You'd need the L-bracket on the camera body that someone else suggested, but that adds cost and bulk.

Note: Which Nikkor AF-P 70-300mm do you have? I noticed there's one without VR... the other with it for about $50 more. This is a situation where VR might be helpful... handholding those shots or even on a tripod. However, higher shutter speeds that you probably need anyway for BIF shots, tend to make make VR less important (and some Nikon shooters turn it off anyway, feel that it slows AF performance).

Finally, are you certain it's "camera shake blur" you're seeing? Too slow shutter speed also can lead to "subject movement blur", which even the sturdiest tripod setup in the world can't help resolve.

"Unsharp images" also may be due to missed focus. I don't use modern Nikon gear and can't say for certain, but I think the "AF-P" lenses use a "stepper motor" to drive the AF, similar to Canon's "STM" lenses. In the Canon system those are faster than cheaper micro motor lenses, but "USM" or "ultrasonic motor" lenses are 2X to 4X faster focusing than STM/stepper, making the USM/ultrasonic much more preferable when shooting moving subjects. The stepper motor lenses just can't maintain focus lock on faster moving subjects as well. I think "AF-S" Nikkors use a "Silent Wave" ultrasonic focus drive system that's comparable to Canon's USM. Most sports/action shooters look for ultrasonic focus drive... I sure know I do!

My point, though, is to be sure that you're addressing the actual problem.

I've been getting serious about shooting BIF for some time now. All of my practice has been hand-held. One or two images have been sharp, but not tack sharp. I'm shooting with a Nikkor AF-P 70-300mm on a D7100. After my last outing I decided that I needed to be using a tripod. So began my search for a head. What I discovered is that because my lens does not have a lens mounting collar, a Gimbal head simply won't work. I didn't realize that when using a Gimbal head, the lens attaches to the head rather than the camera being attached to the head. My question for the experts is: is there a ball head that can be used on my very substantial Manfrotto tripod that will enable me to follow BIF with almost as much smoothness as the Gimbal head? I've never seen a ball head in use, but have perhaps an unfounded perception that a ball head cannot come close to the smoothness of a Gimbal. Surely, for those of us who do not have long lenses that have mounting collars, there must be something on the market that will enable us to do BIF with 300mm collarless lenses. Thanks for your help...Bunkershot