Ok. So it's established that it is Mullberry.
I've not honestly harvested wood specifically for bow making. I have far large format carving (Search "carving Benedict in Maple" on Youtube. that came froma log of maple that was hip high on it's side).
This is what I would do.
cut out the straight sections. Longer is better but even if you have some that are "short" you can splice them so after the longest premium sections are cut look for anything 36" - 40" and cut those out also.
Depending on size I would quarter the log at least and leave the bark on. Put it in a garage or basement or something where it can dry but not TOO fast. Keep it off the ground and paint the ends with cheap latex paint and possibly give it a mist of insectocide. Some carvers will wrap the wood in plastic and fume it with paint thinner to suffocate what ever may be in or under the bark. I haven't done that and never had a problem with anything that I dried in the garage and off the ground. If you see signs of insects kill em as mentioned above. I sprayed my wood with paint thinner... Grubs come running out of the holes and then die. That was a log of oak I started drying outside.
After several months the wood will shrink and the bark will naturaly seperate... or at least that has been my experience.
Unless you don't have access to a large bandsaw and or prefer to split it down to wedges I would quarter saw it into 1 3/4 (or so) slabs or "flitches". (there are attachments for chainsaws that do a great job of this on Ebay for $20.00). When you stack the wood to dry put skinny spacer between the boards. The thinner pieces will dry faster. The Quarter sawing recudes the tensions as it shrinks with reduces cracks and such. It may be able to be roughly split in a quarter sawn fashion.. I have never tried.
When it is dry you have a slab of bow blanks and backings. Pop off the bark and band saw from the bark edge the core or belly pieces you want by either cutting them straight and planning to back them OR follow a grain line +2 or 3. Each blank will have idealy oriented grain.
There is video on YouTube under Bickerstaff bows "how a bow is made" vid# 3 or 4 I think. He's talking about hickory but the concept is the same. It is a pretty efficient use of wood I think.
BTW that "V" splice is plenty strong and much faster/easier than a "W" splice.
Just my$.02
now... How do I get my hands on a segment say 36-40" long?