In principle, the BIG-IP will interoperate with ASA devices running current ASA software and a current TMOS versions. It is frequently done in fact, but requires patience and sometimes assistance from F5 Support. IPsec is hard to wrap your head around.
Both IKEv1 and IKEv2 are supported when bringing up BIG-IP tunnels to an ASA, although you really do want to be running the latest version of 13.1. For an ASA interop, right now I'd recommend starting with IKEv1. Disclaimer: Most vendor specific Vendor IDs are not supported by the BIG-IP.
Unless you're configuring a BIG-IP in the Cloud (Azure/AWS/Google) then I recommend you configure your IPsec Policy (net ipsec ipsec-policy) to use "Tunnel" mode. Do not use "Interface" mode, it is more complex to configure and is useful only for very specific solutions. From the ASA's perspective it won't have a clue whether you've selected Interface or Tunnel mode and it is not part of the ISAKMP negotiation (tunnel setup).
Following a guide like this should be fine:
https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/tmos-implementations-11-5-0/17.html
It takes the assumption that you are configuring two BIG-IPs as peers, so just pretend that "BIG-IP B" is the ASA!
That manual chapter is missing one important point. If you don't have a default route, or you have multiple gateways, you need to configure a static route for (1) the next-hop to the remote peer's public IP and (2) the next-hop to the remote peer's private network. If I recall correctly, the ASA has a similar requirement. The next-hop IP for both route (1) and (2) will be the same IP. Yes, you read me right, tell the BIG-IP that the route to the private network is via your ISP next-hop.
Don't forget that if either side is behind a NAT, then enable NAT detection.