Nice work on that Bicone and your problem may be these antennas are not 50 ohm, they are usually in the 150-300 ohm range and the element angles have influence on the impedance. It probably has a good match somewhere over a narrow range in the lower VHF band (in the fat dipole mode) by looking at its size.
I've been playing with Bicones for the last few weeks and just put up a modified military OE-354 and a Harris RF-9070 shown in the pictures below.
The OE-254 is originally a 30 to 90MHz antenna and I extended the six 8' 6" elements to 10' and now it covers down to about 25Mhz or so. This thing kicks butt on 10m and 6m!
The Harris RF-9070 covers about 90 to 470MHz with a little gain and each element is 48" long and the whole antenna stands about 6ft tall.
Each of these antennas has a matching network in the hub and the OE-254 has a modified 4:1 balun with a capacitor on the input to lower the impedance range. The Harris matching network is in inside the hub and I haven't looked at that one yet.
I also have a Nevada Double Discone which is a Bicone without any matching network and its about half the size of the Harris even though they claim (or lie) that it covers 25-1300MHz. It doesn't work as well as a RS Discone and the match is terrible except in the 2m ham band.
prcguy
Note:
The first antenna to the right of the big Bicone is the top of a 6dB ish gain 225-400MHz antenna, the next one to the right is a dual band 118-136 and 225-400MHz, the next to the right is a KRECO 100-800MHz Discone the the other Discone is an Astron rated 100-400MHz but it goes much higher.
I maid this bicone antenna with car antennas from a local scrap yard and I don't understand why it does'nt work very good, compared to a discone antenna (factory maid) it yield only poor results.
The elements are 29 inches long.