QUIT BLAMING BARTLETT. THE CLIENT SETS THE RATE! 
Bartlett has overhead costs and skims ~15% off the top of your rate. 
(WARNING MATH EXAMPLE AHEAD) 
WinoNuclear is having an outage. BNI bids to provide support for the outage along with other companies.
The RP techs are paid $30/hr and the utility is billed at $45/hr. (not including PD) 
The RP techs are paid $45/hr for overtime and the utility is billed $45/hr. 
Based on an outage workweek the RP tech grosses $2640. 
BNI grosses $3240, a net of $600/week.
Out of this $600/week-technician, BNI must pay multiple support people (office workers and support staff) and business development costs.
You have the right idea, but are missing some key points that I have mentioned before. As a small business owner myself, I have to pay myself payroll, as well as others.
Lets say your pay rate is $30/hr. (Which is set by the utility, not the vendor)
There is around 30% in additional costs directly related to that pay rate (Uncle Sam related expenses), and about 10% for company overhead, for a total of 40% multiplier required to staff a position with no profit. An additional 10% profit is common. Some times the profit is 5%, depends how bad they want to win. So you are talking about $1.5/hr profit on your $30/hr pay. Maybe $3/hr profit on a "fat" contract.
Lets say you work for a vendor at a site for a year. The vendor pays you for 10 vacation days and 11 holidays. That means the vendor can only bill for 1912 hours, but has to pay you for 2080 hours. Or $62,400 in payable wages, but only $57,400 in billable wages. There is FICA that the employer pays in addition to what you pay, of 6.2%. They pay an additional 1.5% to medicare. They have to pay into the state unemployment tax/insurance, then they have to pay Federal unemployment tax/insurance. The worst other than FICA, is workers comp, which can be 5%, or as much as 20% for higher risk job titles.. like anything with nuclear or radiation in the title. Then there is General Liability insurance which starts at 2%. Then you add in payroll processing, loan on payroll (you know, cause they pay you NOW, but don't get paid by the client for 90 days. Add in PPE and drug tests. Some times even medical insurance and 401k match... but lets be realistic.
So:
9% for Holidays/vacation.
6.2% FICA
1.5% Medicare
1.3% Federal/State Unemployment
10% Workers Comp
2% General Liability
2% Payroll Processing/Loan
32% Sub Total
So, at 32% 'Direct Costs', they are taking a LOSS, because none of that includes overhead of %12%. 44% would be break even, anything above that is profit. The costs vary a little from company to company, but those numbers are a good thumb rule. Some job titles have higher Workers Comp rates, it varies on the job title, the state, and your carrier. Other numbers could get better like not having to finance payroll, and slightly lower liability insurance. The big numbers are very consistent though. The larger companies may get a small advantage over the small companies on factoring payroll or insurance, but they have to make up for it with a larger staff/overhead, so the bottom line is about the same.
$30.00/hr pay rate
$9.60 in Direct costs
$3.60 Overhead
$3.00/hr profit
$46.20 billing rate.
You had $30 and $45 which sounds reasonable, but $3/hr * 72 hrs during an outage week is only $216/wk profit. Even if you counted 'overhead' as profit, which you cant, it would only be an additional $260 a week for overhead. You know, those recruiters, people in payroll, and managers. There cost is real, not profit.
So, on a 40 hr week, the vendor has to pay out of pocket $1200 to you, $384 in direct costs, $144 in overhead a week NOW ($1,728) to bill the client $1,848 in 90 days to get $120 in profit. I don't know about you, but I could make a better ROI in other ways with less headache.
