My advice is to pick the one that's more immediately comfortable to you and stick with that. There are things that each bow does naturally that the other bow has a harder time with, but ultimately you'll be able to do pretty much anything you want on either bow.
Also +1 to carbon fiber: fiberglass bows aren't great, and wood bows under $1000 can be really hit-or-miss. Carbon fiber bows are generally thought to have a bit less complex of a sound as wood bows, but at the sub-$1000 price point they usually respond and feel much better than less expensive wood bows, which if you're just starting with the bow I believe is more important.
Are you currently seeing your bass guitar weekly? If you are and you want to commit to doubling my recommendation is to see each teacher every other week. I think double bass requires more consistent reinforcement of technique in the early-to-intermediate stages of playing, and I think a month between lessons is too little hands-on time with your teacher. I definitely don't think you should give up bass guitar lessons entirely either. I echo what others have said: even though both instruments have "bass" in the name, have the same function in their respective genres, and have the same notes, the approach to both instruments is vastly different and it will require dedicated focus on both, at least initially.
