Is there a number?
No. A firm of thirty that bids two a month is not disciplined by default. It may be bidding two that fail the gate, every month. A firm that bids eight a year and wins four may be healthier than a firm that bids twenty and wins four. Cost per win will tell you. A blog with a number will not.
Near-zero competition on this query is not a reason to invent a benchmark. Capacity planning is arithmetic from your roster and your rates, not a percentile.
How do you plan it?
Name the people who write and the people who deliver. Count the hours a pursuit actually takes, not the hours you wish it took. Multiply by the number you are tempted to start. If the product is a quarter of the principals’ year, you are not bidding. You are closing the firm for a season.
The default 40 hours is a floor. Defence, consortium, multi-state facilities: higher. Panel RFQs: sometimes lower, until you count the expected volume. Be honest. Then decide how many nos the gate must produce for the year to close with a roster still standing.
What if twelve arrive in one week?
That is a discovery problem or a saying-yes problem. It is not a reason to skip the gate. Skipping the gate is how twelve becomes twelve drafts. Twenty minutes each, one inbound at a time, mandatories first. Several will die on day one. That is the system working.
If you cannot staff the twenty-minute slot, you cannot staff the responses either. The slot is cheaper. Run it.
How does this sit with utilisation?
For consultancies the constraint is billable hours, not headcount. See the utilisation trap. For facilities firms the constraint is estimators and the volume of thin-margin work. Same logic, different roster. Bid what fits. Stop counting submissions as health.
A clean no, in week one, returns the week and tells the buyer what you are for. The firms that decline well get asked back for the work that fits. The firms that submit thinly get asked back for the work nobody else wanted.