The basic formula is: TX Size = (#Inputs * 148) + (#Outputs * 34) + 10
Outputs is easy... basically how many addresses are you sending to? You said 3000... so that part is sorted.
For the inputs, you would need to see how many UTXOs you currently have in your wallet... and figure out the minimum number of UTXOs that you would need to use to get to the required amount you need to send + fee. Unfortunately, I can't see any API call that would assist with this part... so you'd need to go through your wallet manually to figure it out. For each UTXO you need to use, that equals 1 input. So, if you needed to use say 20 UTXOs to get to the required amount, you'd have 20 inputs.
Then you can just pop those two numbers into
mocacinno's fee estimate, Option #2 and click estimate...