I was not there when you went over BSP.
OK, so BSP works and is priced as per the BattleMech Manual. You guys currently have access to ASF support (offensive and defensive) and artillery; you don't have access to minefields. For completeness in certain defensive missions, you can also use your combat engineering vehicles to construct fortifications, though ya'll are rarely on the defensive.
Each ASF can make a single sortie TYPE per mission, and may make that sortie up to twice (50+ ton ASFs are "heavy", others are "Light") per game. Each Artillery piece may fire twice. Each INDIVIDUAL use of a support asset is priced individually. If you have two Sniper Artillery guns, and each one fires twice, that costs 16 BSP (4 points per shot).
Here's the cost table. Attached below is the Aerospace Rules Revision which gives us greater fidelity to the Aerospace support process (and a chance to actually shoot down ASFs); it doesn't change any BSP costs, but does include things like "how many bombs are used in a Bombing Attack".